My best friend is a woman. We hang out together all the time and I love her dearly, but we're not physical with each other. We're both very tactile, so there's a lot of hugging and stuff, but no sex. Or anything close to it.
What I'm getting at is that my best mate and I behave the same way that you (LuckyStar) seem to be looking for... but she's not my girlfriend.
I honestly believe that sex (and other assorted firkyfoodling) is the one thing you do with your significant other that you don't do with anyone else. If you're with someone that you don't have sex with, what you have is a really good friend. Nothing wrong with that, in fact there's everything right with that, but they aren't your partner.
Not in my humble, anyways.
