Start a Conversation With a Girl By Asking a Favor
You are at a bar and you have moved next to that pretty girl.
A conversation starter might be, "Excuse me, but would you mind handing me a napkin over there?" (Make sure the napkin is in reach.)
In my experience this does a few things.
1) It opens up a conversation without a corny pickup line.
2) It allows you to see her reaction to an "innocent" favor.
3) You get to touch her when the napkin is passed (although only brave Don Juaners will try for the hand hold at this point).
4) By requesting a favor from her, you are now "obligated" to her ever so slightly. She will unconsciously be aware of this and you can use it to your advantage.
Keeping with the example above, you could start small talk by saying something clever like, "Did you know that simple napkins can be special?" and then proceed to make her a paper rose. Or you can try paybacks by saying, "Hey, thanks for the napkin. I noticed that your drink is almost empty, would you care for another one?"
The idea is called reciprocation and every culture has it. Use it to your advantage. Remember, keep the "favors" small and simple - may I have a cigarette? May I have a napkin? Would you pass me a straw?