Brock of Pewter City:

RB:
Geodude LV 12
Onix LV 14

Y:
Geodude LV 10 (Tackle)
Onix LV 12 (Bide, Bind, Screech, Tackle)

RBY:
You recieve the Boulder Badge, TM34 (Bide), and the abillity to use Flash wherever you want, once you defeat him of course.

Use:
Your best bet is to rely on a water or grass type Pokemon. If you are playing Yellow, then use Butterfree's Confusion(LV 10), or Mankey's Low Kick(LV 9). Electric Pokemon won't even make a dent, so don't try it(that means Pikachu!).

Misty of Cerulean City:

RB:
Staryu LV 18
Starmie LV 21

Y:
Staryu LV 18 (Tackle, Water Gun)
Starmie LV 21 (Bubble Beam, Harden, Tackle, Water Gun)

RBY:
You recieve the Cascade Badge(Pokemon LV 30 and below obey you), TM11 (Bubble Beam), and the abillity to use Cut whenever possible.

Use:
Electric Pokemon have a good advantage against Water Pokemon. But, if you rely on Pikachu to much, it'll get weak against the strong blasts of water. Using Grass or another Water Pokemon work great as well. I suggest getting a Oddish or Bellsprout for your match.

Lt. Surge of Vermillion City:

RB:
Voltorb LV 21
Pikachu LV 18
Raichu LV 24

Y:
Raichu LV 28 (Growl, Mega Kick, Mega Punch, Thunder Bolt)

RBY:
You recieve the Thunder Badge, TM24 (Thunder Bolt), and the abillity to use Fly in or out of battle.

Use:
Ground or Rock Pokemon work good against this gym. I suggest getting a Diglett or Dugtrio that knows Dig for this battle.

Erika of Celadon City:

RB:
Victreebel LV 29
Tangela LV 24
Vileplume LV 29

Y:
Tangela LV 30 (Bind, Constrict, Mega Drain, Vine Whip)
Weebinbell LV 32 (Acid, Razor Leaf, Sleep Powder, Stun Spore)
Gloom LV 32 (Acid, Petal Dance, Sleep Powder, Stun Spore)

RBY:
Once you defeat her, you'll recieve the Rainbow Badge(lets Pokemon up to LV 50 obey you), and TM 21 (Mega Drain).

Use:
Fire Pokemon work good against this gym. Or you can use Grass types that know moves non-plant-related.

Sabrina of Saffron City:

RB:
Kadabra LV 38
Mr. Mime LV 37
Venomoth LV 38
Alakazam LV 43

Y:
Abra LV 50 (Flash)
Kadabra LV 50 (Kinesis, Psychic, Psywave, Recover)
Alakazam LV 50 (Psychic, Psywave, Recover, Reflect)

RBY:
Once you defeat her, you'll recieve the Marsh Badge(lets Pokemon up to LV 70 obey you), and TM46 (Psywave).

Use:
Bug Pokemon seem to work pretty good. Ghost types are immune to certain kinds of attacks, but aren't to good against psychic. You could always skip this gym and come to it later when yo have better Pokemon.

Koga of Fuschia City:

RB:
Koffing LV 37
Muk LV 39
Koffing LV 37
Weezing LV 43

Y:
Venonat LV 44 (Psychic, Sleep Powder, Tackle, Toxic)
Venonat LV 47 (Psybeam, Psychic, Supersinci, Toxic)
Venonat LV 48 (Double Edge, Psychic, Sleep Powder, Toxic)
Venomoth LV 50 (Double Team, Leech Life, Psychic, Toxic)

RBY:
Once you defeat him, you'll recieve the Soul Badge(raises your Pokemon's Special), and TM 06 (Toxic), and the abillity to use Surf.

Use:
This gym's Poison and Psychic attacks can have an advantage or disadvantge for your Pokemon. Use Fire types, and Bug.

Blaine(That's the city Goopie lives in. ^_^) of Cinnabar Island:

RB:
Growlithe LV 42
Ponyta LV 40
Rapidash LV 42
Arcanine LV 47

Y:
Ninetales LV 48 (Confuse Ray, Flamethrower, Quick Attack, Tail Whip)
Rapidash LV 50 (Fire Spin, Growl, Stomp, Take Down)
Arcanine LV 54 (Fire Blast, Flamethrower, Reflect, Take Down)

RBY:
Once you defeat him, you'll recieve the Volcano Badge(increases your Pokemon's skills!), and TM 38 (Fire Blast).

Use:
Use strong water Pokemon, like Blastoise or Gyarados. Ground/Rock types have a good defense against this gym.

Giovanni of Viridian City:

RB:
Rhyhorn LV 45
Dugtrio LV 42
Nidoqueen LV 44
Nidoking LV 45
Rhydon LV 50

Y:
Dugtrio LV 50 (Dig, Earthquake, Fissure, Sand Attack)
Persian LV 53 (Double Team, Fury Swipes, Screetch, Slash)
Nidoqueen LV 53 (Double Kick, Earthquake, Tail Whip, Thunder)
Nidoking LV 55 (Double Kick, Earthqueake, Leer, Thunder)
Rhydon LV 55 (Earthquake, Fury Attack, Horn Drill, Rock Slide)

RBY:
Once you defeat him, you'll recieve the Earth Badge(lets ALL Pokemon obey you), and TM 27 (Fissure).

Use:
Water, Grass, and Ice Pokemon work best against this gym. They need to be at pretty high level as well.