I'm going to post a big list from Rank 1 to Rank 15:
1. Bulbasaur/Ivysaur/Venusaur: Basically a gamewinner in-game, featuring lots of support moves and the best Grass Move in Gen I (Razor Leaf), it can help you even in gyms when it's at type disadvantage. With Chlorophyll, this thing is even more monstrous when it can demolish pretty much anything in the sun, especially with the Growth buff.
2. Mudkip/Marshtomp/Swampert: Not just a meme - its only weakness is nearly nonexistent on Hoenn trainers, it can take many hits thanks to its bulk and has strong coverage. It can even use Surf, Strength, Rock Smash, Waterfall and Dive if you need HMs. It did worsen in competetive play, but it's still good.
3. Torchic/Combusken/Blaziken: Basically, when you want to disregard bulk and stalling and prefer to wreck everything, Torchic is the right choice. It's also a ferocious murder machine with Speed Boost, however, one miss with Hi Jump Kick and all you got is fried Chicken.
4. Totodile/Croconaw/Feraligatr: Sprout Tower slows it down quite a bit, but it can easily catch up in Union Cave. Also, it's a good Surf user, as I have a hard time to find something to give the HM to in-game. Finally, Dragon Dance can make this thing a beast in multiplayer.
5. Piplup/Prinplup/Empoleon: Unfortunately, all of the Sinnoh starters are fairly mediocre in-game (due to the insanity that is Staraptor), however, it has unmatched offensive strength in rain compared to the other starters, using Agility, Substitute, Petaya Berry and Torrent for maximum ownage.
6. Cyndaquil/Quilava/Typhlosion: Makes the in-game portion of Johto a breeze - however, it is slow in learning strong Fire moves, although you get Flamethrower or Fire Blast in Crystal and HG/SS respectively upon entering Goldenrod City. It can also take a stray Fire move with Flash Fire and blast everything with Eruption.
7. Snivy/Servine/Serperior: It's fairly good in-game, featuring good set-up and status moves. Lack of coverage and having a weak typing makes it bitter, though. Competetively, it does fairly nice with its ability, but it's hard to make it useful.
8. Squirtle/Wartortle/Blastoise: While Bulbasaur does well in every aspect in-game, Squirtle outperforms it in attacking prowess, having a better coverage and also a better HM selection. It is a fairly solid Rapid Spin user in versus battles, but it lacks in other areas.
9. Tepig/Pignite/Emboar: It can smash heads in as much as Blaziken does in R/S/E. Its level-up movepool isn't that good. However. it learns nice coverage through TMs (which don't break in that Gen). In multiplayer, it has Reckless to break things, but it doesn't do well due to its low defenses and Speed.
10. Turtwig/Grotle/Torterra: It's slow, but has the endurance and the attacks to fight the in-game opponents very well, although it gets screwed over by Ice Fang/Ice Beam more often than you imagine. In versus battles, it's a nice tank, however, it has too many weaknesses to be effective.
11. Chikorita/Bayleef/Meganium: In theory, its bulk, early Razor Leaf and support moves would make it amazing, but Johto is as friendly to Grass-Types as a battalion of lawn mowers. It can't use its support too well competetively because it doesn't have that many and can't threaten the opponent well enough.
12. Oshawott/Dewott/Samurott: It isn't as good in offense as Emboar and lacks the defensive utilities of Serperior. It's only redeeming quality is that that you don't have to use Panpour for Surf (can't get Basculin or Jellicent without). It does have some nice moves for competetive battling, but is too average to be great at something.
13. Chimchar/Monferno/Infernape: While it does help with Gardenia, its offenses are too low to do significant damage, occasionally losing even to Piplup in the first rival battle. It's much better in competetive play, where it can use its speed to great effect, both to sweep and support.
14. Charmander/Charmeleon/Charizard: It has the same firepower as Cyndaquil, but you don't really need Fire moves at any point in Kanto. It's not better in versus battles, where it is owned due to its common weaknesses and especially Stealth Rock.
15. Treecko/Grovyle/Sceptile: It helps you get through Hoenn as much as the "I hate N'ers" sign helped John McClane get through Harlem. It learns nothing useful until Level 29, where it's still walled by anything not weak to Grass. It is ludicrously fast in competetive play, but lacks attacking power to use it as anything but a sub-seeder.