Don't misunderstand me now, I definitely think video games are wonderful in almost every aspect, and I've played tons of games that touch my heart with their beautiful storylines, music etc - but I almost never feel that I actually personally care for the characters.
I do think characters like Link, Mega Man and Chrono are great, but I never get a real chance to sympathize with them, because honestly they don't have much of a personality.
The game that has come closest to this (and managed very well, I must say) is Ico - I can't put it into words very clearly, but in that game I really felt like I was helping a friend; that's the kind of connection I'm always looking for in a game.
Another game that pulled this off very well was Final Fantasy 9 - except for Quina and Amarant (who were basically the funny guy and the tough guy) I felt a very close connection with all the characters (especially Zidane and Vivi!), and Squall and Rinoa in FF8 also had their moments; but except for these games (who should set an example for other games to come) it is highly unusual to actually feel anything for a video game character.
I seriously think that game developers should think of character development as more of a sort of hobby, and not just something that "takes up time during development".
If they do their best to create characters for their own sake during their free time (which really isn't that hard, they can come up with character ideas in their head during a tedious train trip or something), without any commercial interests, they can use those characters later if they feel like it, when they have got an own feel for the characters and made them "alive", with short background stories and so on.