As clearly many others have said, my favorite would have to be Charmander. My first Pokemon game was actually FireRed (everybody owned a Game Boy back in the day except for me...), and I did a lot of thinking before I got it on which Pokemon I wanted to start with. I finally settled on Charmander - can't remember why, but somehow I thought it was the best selection.
So not only is there the nostalgia factor, but Charmander and its evolutions just seem to have received more love and attention than most other starters. Charizard gets all kind of Claw (Shadow Claw, Dragon Claw, Night Slash), Fang (Fire Fang, Thunder Fang), and Flying moves, especially through Move Tutors and whatnot. All its forms look awesome, and they're fast and powerful to boot.
Another favorite is Turtwig and its evolutions - sturdy, powerful, and eventually very versatile with its Grass and Earth-type moves. I wasn't very fond of Chimchar or Piplup, but Turtwig? Turtwig was a war machine.