Lara Croft is my all-time favorite video game character. I like that she's brave and very intelligent, and is very good at handling the supernatural.
I also like Yoshi, Koopa Troopa, Birdo, and Princess Peach from the Mario games, Pac-Man and Ms. Pac-Man from Pac-Man, Coco from the Crash Bandicoot games, Gilgamesh and Ki from the Druaga games, and Balthier and Fran from Final Fantasy XII.
And even though I'm not a Sonic fan, I do really like Rouge, and I kinda have a soft spot for Cream even though a lot of people don't like her.
My favorite bosses are Bowser from the Mario games and Jacqueline Natla from the Tomb Raider games.