Link, hands down. No matter what game I'm playing, I always enjoy running around as a mute elf in green tights. There's never a point where he's arrogant or otherwise unlikable. He may seem a bit hapless, depending on which game you're playing, but that only makes him more likable. Link has been my favorite character ever since I got into video games, and that's not gonna change anytime soon, if ever.
Honorable mentions go to:
Midna - Possibly Nintendo's best character in a long time. She originally began as one of my least favorite characters in gaming, but how she changes in Twilight Princess is one of the best things to happen in video gaming. That, and she has a wit as sharp as House's, and an even sharper incisor. What's not to love about that?
Travis Touchdown - It's funny how a character with an almost completely different personality than me is one of my favorite characters. An arrogant, nerdy hipster with a kickass motorcycle and a lightsaber knockoff who's in an assassin league. I immediately grew attached to Travis when he asked Sylvia the big question: "If I become number one, will you do it with me?"
Gordon Freeman - Not one of my favorite game series, but still one of my favorite characters. Once again, another mute character in gaming, but still one who remains likable. The decent acting and the storyline really help to place you in this scientist's boots. That, and he has a gun that defies the laws of physics. Pretty cool.