I think most women have had pick-up lines used on them at some point or another. However, some men might argue how else are they supposed to approach a woman without using some kind of a line? And some PUAs (pick-up artists) even recommend you fabricate a story--and have several of these stories up your sleeves ready at any time---or use little techniques like: have the girl hold up her hand and if her ring finger is taller than her index finger tell her that means she is very adventurous, and other dim-witted things like that. I mean, really, unless you want the type of girl who would fall for something like that (innocent and naive) then you should really try for something more realistic and more honest. 

Personally, I really appreciate if a guy can be themselves. In other words, I can't give you a formula that will work on every girl, but anyone can tell when you're being yourself and when you are simply trying to be smooth and act a part. Unless being smooth is really who you are, then that's fine. You see what I mean?

Maybe mention something you noticed about her---something that caught your eye that made you cross the room to tell her. And please skip the obvious and generalities. Stick to specifics and the truth---she will notice and it might just touch her. 

Don't ask for her number. First of all, it's a very awkward and uncomfortable moment for the woman--- what if she wants to say no but feels bad? Say what you want to say to her---"I want to treat you the way you deserve to be treated. Here's my number. Call me." Yes, someone actually did say that to me. Very cheesy, but cute. I was a waitress at the time and had loads of guys ask for my number. (They all seemed to think they were special and the first to ask me out....NOT). I learned to smile charmingly but firmly, and say that "I don't give my number out, but you can feel free to give me your's." Some men chose not to leave it (I strongly discourage that, if any woman ever says that to you---women often keep stuff, and who knows, one night when she's bored she might see your number and call you on a whim), but most did leave their number. But I suggest if you do that first, and don't ask for her number it seems much more gentlemanly and less desperate. 

Of course, every woman has their own personal quirks and preferences. However, I'd recommend you start off being yourself, as it's going to come out sooner or later (your personality, that is) and unless you're looking for regular one-night stands it's best, in the long run, to start off being you.