I'm glad we can finally have a poll where Charmander doesn't kick everyone's ass.
....Anywho! Considering this is in the ANIME SECTION *hint, hint, wink, wink, nudge, nudge!*, I'm going to vote for my favourite starter pokémon in the animé. Yeah, it's an insanely bizarre concept I know, but I'm afraid you'll have to bare with me for a moment here folks.
My favourite animé!starter pokémon was Treeko.
Treeko was a really great character, and one of the few pokémon to develop a personality you could actually sympathise with. Treeko was a loner, who didn't take help from anyone, and lived by his own rules. He pushed himself to his limits on a number of occasions, and always strived to reach his full potential, no matter what obstacle stood in his way. It didn't matter if he couldn't use any grass type moves: He was going to flatten that far more experienced Hariyama. He couldn't care less about sticking around with Ash, as long as he could get his rematch with the rampaging Exploud. Screw that Beedrill swarm, I'm going to dive right in there despite the fact I can't even attack.
That's what I really admire about the pokémon the most. He worked his bushy fern butt off to get where he is today. It was by no means an easy ride, and he did in fact have it a lot tougher than pretty much any of Ash's other pokémon. But at the end of the road, he's wound up being Ash's strongest grass type (and no, that ISN'T debatable), as well as being one of his toughest contenders overall. And he truly earned it.
I also liked his relationship with Ash and the other pokémon. He loved his trainer like everyone else, but had a very subtle way of showing it due to his preference of solitude. I rather liked the fact that he was one of the few pokémon to never charge up to Ash and hug him in some comical fashion, or pound him with an attack to show his affection.
Runners up include-
Chikorita/Bayleef, for not only looking and sounding as cute as a button, but also for having a very entertaining relationship with Ash.
Torchic, for being a complete and utter stooge and (as Yamato-san pointed out in an earlier thread) being the first starter pokémon to actually represent a begining trainer's first partner somewhat accurately.
Cyndaquil, because it's behavoir and attitude were downright odd most of the time. One moment it would be full of energy, the next it would let out a big yawn of sleepy content. That and the fact that it is easily the most underated starter pokémon to ever grace this show. Far too many people seem to love throwing around the false rumour that Cynda was one of Ash's weakest, when this was clearly not the case.