(Note: stardates sometimes seem to be messed up somewhat, but i'm mentioning events in the order they're mentioned in Chronology. Where stardates are not given, none were mentioned in the episode.)
2364 ST:TNG first season, including the first encounter with Q in "Encounter at Farpoint." (sd. 41153)
Lt. Denise Kallerinth assigned to Enterprise, brings Jax DeSabel with her (just prior to "Where No One Has Gone Before")
Wesley Crusher, Sam Lator, and Jax DeSabel become friends.
Also in season one, Wes Crusher becomes an acting ensign in "Where No One Has Gone Before" (sd. 41263) in which we also meet the Traveler; the Ferengi are introduced in "The Last Outpost" (41386).
Sam Lator's parents depart Enterprise, agreeing to let Sam stay on the ship.
Lore is introduced in "Datalore" (sd. 41242); Tasha Yar dies (the first time) in "Skin of Evil" (sd. 41601); an extragalactic conspiracy is discovered in which Starfleet has been infiltrated in "Conspiracy" (sd. 41775); first contact with the Romulans since the Tomed Incident in "The Neutral Zone" (sd. 41986).
2365 Guinan comes aboard the Enterprise. ST:TNG season two, Beverly Crusher becomes head of Starfleet Medical; Katherine Pulaski becomes the Enterprise's chief medical officer; Troi is impregnated by some alien energy-being and has a child, all this in "The Child" (sd. 42073). The introduction of the holographic Dr. Moriarty in "Elementary, Dear Data" (sd. 42286).
Odo becomes a security investigator for Gul Dukat on Terok Nor.
JAG Phillipa Louvois rules Data to be a sentient life-form with full rights pertaining thereto in "The Measure of a Man" (sd. 42523); first contact is made with the Borg 7,000 light-years from the edge of Federation space, in the uncharted J-25 star system in "Q Who?" (sd. 42761)
Sam & Jax become acting ensigns; they begin mission to 20th Century Earth.
Boulder & Nuggit are created, by Jax & Sam.
We meet K'Ehleyr in "The Emissary" (sd. 42901), a special Federation emissary who's supposed to intercept Klingon sleeper ship T'Ong near the Boradis system and bring them up to speed on the whole 'Federation and Empire are allies now' thing. She and Worf used to be an item, and they briefly rekindle their old romance, resulting in the conception of a son.
2366 Pulaski leaves, Crusher returns to the Enterprise. Development of the Defiant-class begins.
ST:TNG season three. Nanites evolve into a sentient species and are given colonization rights on Kavis Alpha IV in "Evolution" (sd. 43125); a Ferengi shuttle is lost in the Delta quadrant via the unstable Barzan wormhole in "The Price" (sd. 43385).
Cardassian Wars end.
All kinds of weird-ass temporal stuff happens in "Yesterday's Enterprise" (sd. 43625), including a whole new timeline where the Federation is at war with the Klingons and is in really bad shape, but at least Yar never died. So Guinan says she should be dead but her death was meaningless, so Yar goes over to the Enerprise-C which had shown up from the past, and they all go back in time again and help the Klingons fight off the Romulans at Narendra III in 2344, thus restoring the proper timeline. Sort of. Lal is created by Data, and soon after, more or less dies in "The Offspring" (sd. 43657); Worf accepts discommendation in "Sins of the Father" (sd. 43685), wherein it is alleged that his father, Mogh, had betrayed the Khitomer outpost to the Romulans. It is discovered that in fact it was Duras's father Ja'rod who did so, but that is kept quiet to prevent civil war. In "Captain's Holiday" (sd. 43745), Picard meets archaeologist Vash and they dig up the Tox Uthat, a weapon from the future which was hidden in 22nd century on Risa to keep it from Vorgon criminals, and ultimately Picard destroys the device. Reginald Barclay and his holo-addiction are introduced in "Hollow Pursuits" (sd. 43807). Zibalian trader Kivas Fajo kidnaps Data for his private collection in "The Most Toys" (sd. 43872). We see Sarek again in "Sarek" (sd. 43917), in which it is found he is suffering from Bendii Syndrome. Picard mind-melds with him to lend him some temporary emotional control. Wes Crusher is given a field promotion to full ensign in "Menage à Troi," (sd. 43930) which also introduces the concept of oomox; the Borg attack the Federation, Picard is abducted and turned into Locutus in "The Best of Both Worlds, Part I" (sd. 43989).
2367, ST:TNG season four sees the Battle of Wolf 359 in which 39 Federation and Klingon starships and 11,000 personnel are lost, Picard is rescued, the single attacking Borg vessel is sort of tricked into self-destructing in "The Best of Both Worlds, Part II" (sd. 44001).
Data and Lore's creator, Dr. Soong, dies in "Brothers" (sd. 44085) in which Lore also steals the emotions chip Soong created. In "Reunion" (sd. 44246), Worf meets his son Alexander, Duras kills K'Ehleyr, Worf kills Duras, Klingon Chancellor K'mpec dies, leaving Gowron as the sole contender to become the next Chancellor of the Klingon High Council. Worf's adoptive parents, Sergey and Helena Rozhenko, take custody of Alexander. Wes Crusher goes to the Academy shortly after "Final Mission" (sd. 44307); Spot is first seen in "Data's Day" (sd. 44390); the Cardassians are introduced in "The Wounded" (sd. 44429); Mirasta Yale and Malcor III are introduced in "First Contact." (no stardate given, but it's between 44502 and 44614)
Curzon dies, Dax is transplanted to Jadzia.
Reg Barclay goes to "The Nth Degree" (sd. 44704); Worf utters the line, 'Captain, I protest. I am not a merry man,' in "Qpid" (sd. 44741), which also sees the return of Vash (introduced in "Captain's Holiday) who goes off exploring with Q. "The Drumhead" (sd. 44769), um... provides a quote for the INFO newsletter, or something.
Telek R'Mor, now of the Romulan Astrophysical Academy, dies, like four years before he would have delivered Voyager's messages to Starfleet.
Sam, Jax, Nuggit, and Boulder finish their mission to the 20th century, and Sam and Jax go to Starfleet Academy, where they meet Alex Franx.
Kriosian rebels seek independence from the Klingon Empire. Governor Vagh of the Klingon Kriosian colonies charges the Federation with aiding rebel forces with phaser rifles. In "The Mind's Eye" (sd. 44885), it turns out Romulans were behind it.
The Trill are introduced, in the decidedly more ridgy and less spotty than most Trills form of Ambassador Odan, in "The Host" (sd. 44821). Gowron becomes Chancellor in "Redemption, Part I," (sd. 44995) in which Duras's sisters Lursa and B'Etor declare that Duras's illegitimate son Toral will challenge Gowron's claim to the leadership of the High Council, and it is discovered that Duras's family has been working with Romulans and plotting a civil war within the Empire. and Gowron restores the honor of the family of Mogh (Worf and Kurn). Also in this episode, Worf resigns from Starfleet. A civil war begins between Klingons loyal to Gowron and those loyal to the family of Duras.
2368 ST:TNG season five introduces us to Sela in "Redemption, Part II," (sd. 45020) in which Starfleet manages to cut off the Romulan supply lines to the Duras-loyal Klingons, ending the war. We also meet Romulan commander Sela, daughter of Tasha Yar from an alternate timeline. Worf is reinstated as a Starfleet officer. "Ensign Ro" (sd. 45076) is introduced; Molly O'Brien born in "Disaster" (sd. 45156); Sarek dies in "Unification, Part I," (sd. 45233) in which we also see Spock again, now an ambassador, who is on Romulus working toward a Vulcan/Romulan reunification. Matt Frewer was in "A Matter of Time," (sd. 45349) and it's always fun to see him, especially if he's playing a guy with a name like Berlinghoff Rasmussen. Speaking of kool guest stars, Kelsey Grammer was in "Cause and Effect," wherein the Bozeman is freed from that temporal causality loop (sd. 45652). Wes Crusher & friends penalized for Kolvoord Starburst maneuver, Nick Locarno expelled in "The First Duty" (sd. 45703) (which is to the truth, as any first year cadet could tell ya).
Elim Garak exiled to Terok Nor.
Hugh is introduced in "I, Borg," (sd. 45854) and after that Hugh transfers a sense of individuality to a group of Borg, who were then abandoned by the Collective, sometime after which they were "helped" by Lore; interphasing is introduced in "The Next Phase" (sd. 45892); then you've got "The Inner Light" (sd. 45944) which is one of the better episodes (Picard learns to play a Ressikan flute, etc).
2369 ST:TNG season six sees the return of Scotty and the introduction of a Dyson Sphere in "Relics" (sd. 46125).
A Jem'Hadar ship crashes on Bopak III, where a soldier called Goran'Agar survives without ketracel-white before being rescued 35 days later.
In "Schisms," (sd. 46154) folks from the Enterprise are being abducted by some seriously ugly solanagen-based life-forms from a subspace domain. "True Q" (sd. 46192) introduces us to the babe-a-licious Amanda Rogers, who finds out she's Q. Not to be outdone by the Nanites, some exocomps become life-forms themselves in "The Quality of Life" (sd. 46307). In "Chain of Command, Part I (sd. 46357)" Captain Edward Jellico assumes command of the Enterprise while Picard, Worf, and Crusher are on a covert mission to Celtris III, where Picard is captured by Cardassians.
Cardassian Occupation of Bajor ends.
In "Chain of Command, Part II" (sd. 46360) Picard is tortured 1984-style (with four lights in place of four fingers), and eventually rescued by Jellico and the Enterprise, of which Picard reassumes command.
The Bajoran provisional government asks the Federation to establish a presence in the Bajoran system.
Starfleet takes over Terok Nor, which they rename Deep Space Nine, under command of Benjamin Sisko. Enterprise-D goes to Deep Space Nine, where Miles O'Brien transfers to become the station's chief operations officer.
ST:DS9 begins with "Emissary" (sd. 46379), wherein Commander Benjamin Sisko arrives at Deep Space Nine to assume command. He discovers a stable wormhole in the Denorios Belt in the Bajoran system, linking the Alpha Quadrant to the Gamma Quadrant. Bajoran spiritual leader Kai Opaka decides that Sisko's discovery of aliens living in the wormhole fulfills a prophesy, and calls Sisko the Emissary. Cardassians attempt to reclaim part of the Bajoran system, but are thwarted when DS9 is relocated to the Denorios Belt. In "Past Prologue," Lursa and B'Etor attempt to raise capital for another attempt at gaining control of the Klingon High Council. Moriarty returns in "Ship in a Bottle" (sd. 46424), where he is given a holographic environment (which I'm pretty sure he thinks is real) to live in, and explore space and all.
Sam Lator, Jax DeSabel, Alex Franx graduate; they are assigned to Deep Space Nine.
The Tal Shiar is introduced in "Face of the Enemy" (sd. 46519) In "Q-Less" (sd. 46531), Vash is found in the Gamma Quadrant and goes to DS9. Q follows her there. Stuff happens, they both leave I guess, so does some life-form Vash brought with her. Q plays both God and Capra in "Tapestry" (no stardate given, but it's between 46531 and 46578); Data learns to dream in "Birthright, Part I" (sd. 46578). Meanwhile, Worf goes off to look into rumors of a Romulan prison camp in the Carraya system, full of Klingons captured at Khitomer. We find out a lot of races in the galaxy have a common ancestry, if you go back four billion years, in "The Chase" (sd. 46731). Kai Opaka sort of dies in "Battle Lines" (no stardate given). "Suspicions" (sd. 46830) introduces us to Ferengi scientist Dr. Reyga, who is killed in the episode, and who had been developing prototype metaphasic shielding. The clone of Kahless is introduced in "Rightful Heir" (sd. 46852), who becomes Emperor, the first one in three centuries, and serves as the religious leader of the empire, while political power remains in the hands of the High Council. "Second Chances" (sd. 46915) introduces Thomas Riker, who accepts a position on the Gandhi.
Ro Laren leaves the Enterprise for Starfleet's Advanced Tactical Training program.
"Descent, Part I" (sd. 46982) sees the return of the Borg, although they seem different than those encountered in the past.
2370, ST:TNG season seven. Lore is in control of a renegade group of individual Borgs in "Descent, Part II" (sd. 47025), but Hugh and the Enterprise crew thwart his evil schemes, dismantle him, and recover Dr. Soong's emotions chip.
ST:DS9 season two begins.
Kes is born.
Sam Lator, Jax DeSabel, and Alex Franx acquire a runabout, fix it up, rename it the Musketeer.
Sam, Jax, Alex get promoted to lieutenants.
In "Rules of Acquisition" (no stardate given, between 47229 and 47282) the Dominion is first heard of from the Dosi, with whom Quark is negotiating the acquisition of tulaberry wine.
In "Force of Nature" (sd. 47310) it is discovered that continued use of warp drive was causing damage to the fabric of space. Starfleet begins a program to develop new warp engines that won't cause such damage. In "Inheritance" (sd. 47410) we meet an android with the image and personality of Dr. Juliana Tainer (née Soong, née O'Donnell). "Parallels" (sd. 47391) gives us a small taste of some of the many other universes out there. "The Pegasus" (sd. 47457) introduces the Pegasus, or phase, cloaking device. We meet Dr. Mora Pol, the Bajoran scientist who originally studied Odo when he arrived on Bajor, in "The Alternate" (sd. 47391).
Border finally established between Federation and Cardassian Union, including a DMZ.
Maquis is formed.
"Lower Decks" (sd. 47566) sees the return of Sito Jaxa, one of the cadets reprimanded in "The First Duty." It also probably sees her death.
Maquis terrorists capture a Cardassian dreadnaught missile, which B'Elanna Torres reprograms, and is later lost in the Badlands.
"Profit and Loss" (no stardate given) introduces us to Natima Lang and her students Rekelen and Hogue, and temporarily reunites old loves Natima and Quark. In "Journey's End" (sd. 47751) the colonists on Dorvan V relinquish Federation citizenship and agree to live under Cardassian jurisdiction. Also, Wes Crusher resigns from Starfleet Academy and starts traveling with the Traveler. Kang and Koloth die in "Blood Oath" (no stardate given) after Kang kills the Albino. Kor and Dax survive the mission. I believe the Maquis were introduced in "The Maquis, Part I" (no stardate). The Enterprise has a baby in "Emergence" (sd. 47869). Ro Laren joins the Maquis in "Preemptive Strike" (sd. 47941). The first mirror universe episode since "Mirror, Mirror" in TOS, "Crossover" (no stardate given) establishes that the Terran Empire was conquered decades ago by the Cardassian-Klingon Alliance. Mirror Quark is killed; m-Rom inherits his bar. "All Good Things..." (sd. 47988) brings the seventh and final season of TNG to a close. Despite being two hours long, nothing actually happens in the episode, except Picard joining the weekly poker game for the first time, and that isn't until the very end. In "The Collaborator" Vedek Winn is elected Kai of Bajor. The first Federation contact with the Dominion occurs in "The Jem'Hadar" (no stardate) which introduces the Jem'Hadar, who destroy the Odyssey and other Alpha quadrant ships and the New Bajor colony in the Gamma quadrant.
2371 The Starfleet emblem is altered.
ST:DS9 season three begins with "The Search, Part I" (sd. 48212) which sees the first appearance of the Defiant, along with Romulan Subcommander T'Rul, who operates the cloaking device. In "The Search, Part II," Odo finds that he was one of a hundred infant shape-shifters sent out into the galaxy for exploratory purposes. It is also discovered that his people are the Founders of the Dominion. Quark marries Grilka in "The House of Quark" (no stardate). In "Equilibrium" we learn that nearly half the Trill population could successfully be joined with symbionts, if there were enough available. This is kept secret.
Keiko and Molly O'Brien leave DS9 for an agro-biology expedition on Bajor.
A Jem'Hadar infant is studied, as it grows very quickly to adulthood, in "The Abandoned."
Robert and René Picard die in a fire.
ST:Generations. Data installs Dr. Soong's emotion chip. Lursa and B'Etor are killed. The Enterprise-D is totalled. The Nexus is encountered, along with an energy ribbon that acts as a doorway to it. James T. Kirk dies.
Geordi La Forge gets ocular implants to replace his VISOR.
In "Defiant" (sd. 48467) Thomas Riker hijacks the Defiant, making several strikes against the Cardassians, but is prevented from attacking a secret Obsidian Order/Tal Shiar base in the Orias system. Riker is captured and sentenced to life imprisonment at the Lazon II labor camp, while his Maquis accomplices are placed in Federation custody. After the two part episode "Past Tense," records of the Bell Riots will show that Gabriel Bell looked suspiciously like Benjamin Sisko.
Tuvok is assigned to infiltrate a Maquis group.
ST:V season one begins with "Caretaker" (sd. 48315). Voyager is lost in the Badlands, transported along with a Maquis ship to the Delta quadrant. Vedek Bareil dies in "Life Support" (sd. 48498) which also sees the signing of a peace accord between the Bajorans and Cardassians. The Vidiians are introduced in "Phage" (sd. 48532). Subspace communications through the Bajoran wormhole are established in "Destiny" (sd. 48543). Voyager contacts a Romulan science vessel 20 years in the past through a decaying wormhole in "Eye of the Needle." Miles O'Brien dies and is replaced with an almost identical version of himself from three hours in the future in "Visionary" (no stardate). Harry Kim dies and is later revived in "Emanations" (sd. 48623). In "Prime Factors" (sd. 48642) Voyager visits planet Sikaris, where they have folded-space transporters that operate at distances of up to 40,000 light years.
Seska forges an alliance with the Kazon-Nistrim. In "State of Flux" (sd. 48658), Seska flees Voyager and finds refuge with First Maje Jal Culluh of the Kazon-Nistrim.
In "Through the Looking Glass" (no stardate) mirror-Jennifer Sisko joins the Terran rebellion that began in "Crossover." Also, mirror-O'Brien downloads computer files from Deep Space Nine. Mirror Rom is killed; m-Nog inherits the bar. The Tal Shiar and the Obsidian Order attack the Founders' homeworld in the Omarian Nebula in "The Die is Cast" (no stardate) and are badly trounced by the Dominion. "Family Business" (no stardate) introduces Quark and Rom's mother Ishka, and also introduces Benjamin Sisko to Kasidy Yates.
First Minister Kalem Apren of the Bajoran Provisional Government dies, and is temporarily replaced by Kai Winn. Shakaar Edon is later elected First Minister.
In "Facets," Jadzia's friends help her with the Trill zhian'tara rite of closure, allowing Dax's previous hosts to inhabit them and communicate with Jadzia. In "The Adversary" (sd. 48959), Benjamin Sisko is promoted to captain. A Founder posing as Federation ambassador Krajensky attempts to trigger a war between the Federation and the Tzenkethi. Admiral Leyton and other Starfleet officers recommend drastically increased security measures on Earth, which President Jaresh-Inyo rejects as too extreme.
In "The 37's" (sd. 48975), Voyager lands on a planet where they discover a human colony as well as some humans held in cryostasis, who were transplanted here from Earth in 1937 by the Briori, and from whom the current colony is descended. Among them is Amelia Earhart, which explains her mysterious disappearance.
Stuff in darkred text has to do with the series "Enterprise," which may or may not be accepted as officially part of the Star Trek universe.
Stuff in black text can generally be assumed to be part of official Star Trek, usually if not always taken from the Chronology (Michael and Denise Okuda), or the various shows and movies.