I have always wondered where these girls who love avid gamers can be found. They must be in a magical land of awesomeness. Either that or my super-power truly is an uncanny knack for repelling women. Yeah, that's probably it.
Anyway... As it pertains to your topic; The best advice I could give you is to not let such small-minded ridiculousness get to you. Easier said than done, this I know. But, the truest of truths is that if this girl (or any person really) doesn't want anything to do with you based solely on your love for collecting video games, she's just not worth your time. She's not willing to look beyond surface value of a person (ie your life stats, if you will - money, status, hobbies, looks, etc...). It;s been my experience that people like that simply aren't worth having in your life.
Now, as far as how one tells a girl their a game collector. Unfortuantely, even as mainstream as games have become, many people still view it as a "kid thing" and look upon adult gamers and "childish losers". Tis silly if you ask me, but so are very many things in our modern society. In your case mariocaseman, you're clearly more than just a casual gamer and collector. 500+ games and 12 different consoles means you're pretty involved in collecting and playing. Given the negative connection such a hobby has in society, your love for gaming isn't something I'd lead with when meeting a new girl who interests you (if asked about it, be honest - lying in relationships only leads to problems, trust me on that). Bottom line; If a woman doesn't want to be with you just because you have an extensive game collection, let her roll into the past and keep looking for someone who'll accept that about you (and maybe even share in it with you).