With the exception of Gen 6, I've played all the games more than once so uh.. I'll just pick the most recent one I can remember I suppose.
Blue - Bulbasaur
Sure it sucks at battling in Gen 1 but I wanted to use the Brock Through Walls glitch, for which you need a Bulbasaur. It worked and was a ton of fun. Then I dropped it in the PC and never used it again :/
Crystal - Chikorita
It learns Razor Leaf at level
six in Gen 2 that is so absurdly awesome ^_^
FireRed - no clue. Probably the game I've played the most, so it's all blurred together and I have no idea what my current team is on any given run. The only constant is Farfetch'd.
Emerald - Torchic
Torchic is a cutie and I wanted to name it Nuclear in celebration of Aventine's birthday. Other than that, not much of a reason. It stomps the first gym, but so do the other two choices so idk.
Diamond - Chimchar
It's soooo good. For whatever reason, I catch Pokémon way less frequently in Sinnoh
because the region sucks so it's nice to have a Pokémon that can insta-stomp the first two gyms + Team Galactic while I take my sweet time picking my next team member.
Platinum - Piplup
Wanted to do something different from ^, because I've played Diamond a good dozen times and basically pick Infernape for half of them. Empoleon seems kind of meh in battle tbh. Maybe I just got a bad nature?
Black - Snivy
Not really much to say I don't think. It did an okay job.
Black 2 - Oshawott
It's a cutie and that's the one game where I'd advocate picking a water starter since you don't get the Super Rod until post-game for some reason.
X - Chespin
I honestly don't remember the logic behind this, but its final evolution seems to be a decent physical sweeper so I guess I picked well. Run like hell when the birds show up though.
AlphaSapphire - Mudkip