While the protagonists definitely are criminals, I think they are usually depicted in a way that makes them human and likeable. The storyline and their background makes this possible. I don't think anyone would play the games if the protagonists were just random deadbeats with overall psychopathic personalities. They always have two sides in my opinion - and that's why the games are good.

I especially liked Carl Johnson from San Andreas. Niko Bellic was a huge fail though, he was really a scumbag that I couldn't relate to.

Bottomline, it's really more about the characters themselves than the fact that they're part of the criminal underworld. I mean, you can also choose to be an evil nutjob in almost every single role-playing game out there, so what's the difference? That it's fantasy and this is reality-based? 

They have never been about slaughtering innocents, and I don't mind being a somewhat bad guy that kills other bad guys!