I love how no one's actually thought about saying the obvious things that would work, like "You're beautiful =) " Or other such compliments.
Luckily i'm a suave dashing bastard, cunning rogue and lovable scamp...So I don't have to! >: )
In my experience lines like "You're beautiful" don't work. Sure they're great for the women you're already in a relationship with, but starting out it's not that great a line. Women hear that they're beautiful all the time.
In a bar setting what I've found to be a good opener is "Hey, one of our friends is leaving and we need a fourth for darts. Feel like playing a round or two?" Response is usually something like: "Oh, I'm not very good." And I follow with: "That's fine. Rick over there throws like Peewee Herman, and Miho keeps dropping her darts. You'll be fine. Besides, the game is on us."
Having a female in the group helps.
One of my favorites. I walk over to this skinny brunette, and point back at my buddy Eamon. "See that guy? He just broke it off with his abusive girlfriend. I suck at this emotional stuff. Mind talking with him?" The next morning I'm given a big thank you from Eamon with one of those cheeky grins. Lucky bastard.
Actually now that I think about it, I only approach women on behalf of my friends. Usually I'm too oblivious to act, and thus women ask me for coffee/drink/dinner first.