There aren't all that many video game characters whose personality I think I could stand long enough to be best friends with them. Even my favorites I don't think would make good friends. I'll go through a list of my favorites and see if they'd work though...
Zalbag Beoulve (Final Fantasy Tactics) - Has spent his entire life fighting wars with fairly blind loyalty to his family's cause. He's also an incredibly devout religious, which I don't really have that much of a problem with, but I think it could get problematic when making inappropriate jokes. Agrias Oakes would have similar problems.
Pang Tong (historical figure also in the Dynasty Warriors series) - Was sarcastic and seemed pretty chilled out, but was also a bit of an arrogant twat.
Urdnot Wrex (Mass Effect series) - I feel like would mostly think I'm a pussy. He's also a little violent for my taste.
Mordin Solus (as above) - I'm not really sure how long I could legitimately talk to at length about anything. First of all because a lot of what he'd be saying would be a little over my head, and secondly because I think I might have trouble knowing the kinds of shit he gets up to.
April Ryan (The Longest Journey) - Could potentially work as a friend. She can get pretty whiny, but as she's definitely a lot closer to a real person's personality than a lot of characters.
Naoto Shirogine (Persona 4) - Would be pretty cool, but seems to have a hard time taking a joke.
The Robots (Portal 2) - Seem pretty rad. I think I'll go with these guys. Hugs and high-fives all around.