I don't have a girlfriend, but honestly if I did I think It would almost require she be a gamer. I'm a heavy gamer, all my friends are heavy gamers, many of the family members I see around as well. I don't know if I could be with a girl who didn't see my Halfling artificer riding around on her Dire Bear Effegee dual wielding wands with more on chains at either hip and the quick draw feat to make sure I have the right spells on hand as cute.
Depending on how much of a gamer you are, I personally think its important to make sure you are with someone who will game along with you and do it happily. I know of few gamers who only see it as a small part of their life and if a relationship is going to work you have to share the big things. Lucky for me it will be a while before I feel comfortable to look for anyone and it seems like gaming getting cooler is a growing trend.