Is it normal to have sex with my friend?

They other night i went for a few drinks with my friend (girl) and I (boy) ended up going back to hers and kissing etc. but didn't have sex. I find her really attractive and wanted to have sex with her but because we had had quite a few drinks I felt bad and stopped it before we did. Now i well regret that we didn't do it and even though we are still talking and it is not awkward, neither of us have mentioned us getting with each other. I really want to find out what she is thinking and if she wants to have sex with me but it's hard to start the topic. Is it normal to feel this way about her and is it normal for friends to have sex? If so I would appreciate suggestions on how to approach the subject of having sex with her/getting with her last week.