Chocobo/Mog - MP 14 - AP 3500 - The first summon you recieve. It will usually do deathblow, an attack where a Mog riding on a chocobo will attack the opponent, but will also do the attack Fat Chocobo where an 'Obese' Chocobo falls ontop of the enemy. You get it from the chocobos dancing at the Chocobo Farm
Shiva - MP 14 - AP 50000 - Shiva, the Ice Goddess, will do the attack Diamond Dust where she pummels the enemy with Ice. You get her from pricilla in Junon.
Ifrit - MP 34 - AP 60000 - Ifrit uses the fires from hell to do the attack Hellfire. You recive him from defeating JENOVA-Birth on Shinra's Boat.
Ramuh - MP 40 - AP 70000 - Ramuh creates a Mountain then shoots Lightning down at his foes with his attack Judgement Bolt. You get him inside the Chocobo racing room in the Gold Saucer.
Titan - MP 46 - AP 80000 - Titan flips the ground ontop of the enemy with his attack Anger of the Land. Found in destroyed reactor in Gogonga Village.
Odin - MP 80 - AP 90000 - Odin has two attacks, Gunge Lance, where he heaves his spear into a rift in time then lets it fall down on his enemy, and Steel Bladed Sword where he jumps off a cliff on his Horse and slices the enemy in two killing it instantly. He will only use Steel Bladed Sword on weak enemies. Odin is found in the safe in the Shinra Mansion. [The combo is Right 36, Left 10, Right 59, Right 97]
Kjata - MP 110 - AP 140000 - Kjata does the attack Elemental attack which shoots the various elements at the enemy, although I don't think they count as what they are...[I.E. Fire part won't heal a fire monster] Kjata is found in the sleeping forest. [The materia jumps around]
Bahamut - MP100 - AP 120000 - The famous Bahamut Flies down from the sky and blasts his opponents with his signiture attack Mega Flare. You get Bahamut for Beating Sephiroth's Red Dragon in the Cetra Temple.
Alexander - MP 120 - AP 150000 - Alexander blasts a 'Holy' Laser beam at his enemies with his attack Holy. You recieve him for defaeting the snow lady at Great Glacier.
Neo Bahamut - MP 140 - AP 200000 - Neo Bahamut rips his enemies up into the air with him then blasts them with a beam sending them back where they came from with his attack Giga Flare. You recieve him in the Whirlwind Maze.
Leviathan - MP 78 - AP 100000 - Leviathan bursts out of a circle of water then Makes a Gigantic Wave appear and pummel the opponents with his attack Tital Wave. Now they woulden't give such a cool Monster to just anyone so you have to beat all the people on the Wutai pagoda as Yuffie.
Pheonix - MP 180 - AP 180000 - The Pheonix appears to save the day, first it nails the opponents with fire, then it casts Life 2 on Cloud's Party. You get this when the baby condor is born at fort condor.
Hades - MP 150 - AP 150000 - Hades brews up a pot full'o nastyness then shoots the crap in it at the enemy. The attack does damage and casts almost every negative status effect on the enemy. You recieve Hades on the Crashed Gelinka.
Bahamut ZERO - MP 180 - AP 250000 - Bahamut ZERO Flies out from behind a planet, posisions himself in front of the earth and Blasts the enemy with his Terra Flare. You get him from Having Cloud look at the Giant Blue Materia at Bugenhagen's.
Typhoon - MP 160 - AP 250000 - Typhoon is just weird...He inhales a buncha crap sneezes it on the opponents then turns the world upside down. You get him from the Ancient Forest.
Knights of the Round - MP 250 - AP 500000 - The Thirteen Knights attack the opposition with their various attacks. You can only get it if you breed a Gold Chocobo and go to the NE Island Cave.