I'm going to shy away from the most well known ones for a moment, and go for the character that has always astounded me in his simplicity and true-to-life personality.
Pey'j of Beyond Good and Evil is one of the best developed characters in any video game, because he is so lifelike, so incredibly like your own father that it makes the game have even more impact on you. For being an anthropomorphic pig, he fells amazingly real. BG&E is one of those games where the designers obviously try very hard to give you the full experience, and succeed in it largely because of the relationship between Jade, the protagonist and player avatar, and Pey'j.
The banter between the two is fantastically well done, and gives a real insight into what their relationship is like. Pey'j obviously adores Jade and thinks of her as her daughter. This translates into love for the player, since we are, in a way, Jade herself. And it's a love so easily reciprocated.
Whoa, I waxed lyrically there, didn't I?
Villains deserve at the very least honourable mentions, such as Giygas of the Earthbound/Mother trilogy and of course, Portal's own, GLaDOS. I honestly can't decide which is better of the two.
Sora/Roxas (soras alternate personality) from kingdom hearts. Mostly beacause they have very really good story's and the ges themselves are fantastic making the characters all the more love able.