First gen: bulbasaur because of gym leaders.
Strong against rock, water, lightning, and ground.
Matched by grass and poison (hah! Try to use toxic on THAT, Koga!).
Weak against fire and psychic, but those two are kinda late in the game anyway.
Yellow: I didn't get a choice. And I hated that pikachu. HATED IT! Blastoise had good def and could kick butt. Venusaur take hits fine too and I found his movepool pretty decent due to crits, sleep, and being the only starter pokemon with a healing ability, even if it's a very gradual one. Charizard couldn't take hits as well but he was a major damage dealer and he could FLY in yellow! Have you tried to hit something that could FLY?! It's hard! But Pikachu? Lousy def. Attacks missed most of the time (or was I just unlucky). Kept bumping into me when I wanted to turn around. Wasted time at poke centers just to walk up to the counter. And it wouldn't even let me evolve it. It guilt tripped me every time I put it into its box! (I'm a bleeding heart...) So in the end, it was a useless little mouse that took up one perfectly good pokemon slot that could have been occupied by someone else! Like dragonair. Or Nidoking. Or Zapdos...
Second gen: cyndaquil for the same reason.
Strong against bug, steel, and ice (well, it was supposed to be, but the ice pokemon used are part water and part ground so that sucked, but at least that was late in the game).
Neutral against flying, normal, ghost, and fighting.
Weak against dragon(?) and the flipside of those ice pokemon. Rackemfrackem.
Didn't buy any games after that. 151 was doable. 251 was still plausible. 351 was where I drew the line. And you guys may mock me for picking pokemon strong against the gym leaders rather than taking the underdog approach, but here's my rebuttal: I didn't have to spend as much time grinding for exp. So hah, I say. Hah!