Honestly, I'm a bit shy with women. Why, you ask? Because I realize that women get hit on all the time (most of it unwanted). So to me, strangely enough, women have lots of incentives to talk to guys first. That being said, I still believe in more chivalrous things (holding doors open, etc.) - just when I know a girl's comfortable and interested in me.
I'm different-minded when it comes to relationships. I like meeting new people, and if I don't see it going somewhere with someone, then I'll be forthright about it. My policy: it's better to be honest with people upfront. I don't really understand the idea of being unable to tell someone that you don't want to date them - seems really inefficient and rude.