Yes it's possible to be platonic friends with the opposite sex, but I think about the only way this can happen is if the relationship is casual, and neither one is attracted to the other person in that way. This doesn't happen very often, and things can change though.
I have a few female friends from work, but they are older, married, and I don't spend an excess amount of time with them either.
The really close friendships between males and females like the OP described, I would worry about. There is a very good chance that one, or both are/have been attracted to each other, but didn't get any further for whatever reasons. It's usually the guy that has a thing for the girl, and she see's him as "just a friend", but sometimes, it's the other way around.
If your dating someone, and they are closer, get along better, and get more of their emotional needs from another person of the opposite sex than they do you, then you have a problem.