Looking at a girl, I am generally initially turned on by looks. Though what I think is attractive isn't always conventional, it is a definite factor. Othewise in won't work. If that is coupled with an interesting personality then I'm interested.

When I say an interesting personality I mean someone opinionated, generally interested in things like politics and such. I don't actually concern much over whether the opinions line up with my own. In fact, most of the girls I've found intruiging, (another thing I need,) have had very different views than my own.

It needs to be someone that I can talk to intelligently about things as well as just to talk and be interested in things like the occurences of the day or anything trivial, really. She needs a sense of humor and a distinct personality.
I put a heck of alot of value in being able to talk with the person.

There are some people that I've thought were attractive and got to know them and lost all desire for them. And I've met girls that at first I didn't look at as all to attractive and eventually saw more beauty in them. In that situation it lines up alot with what Adam and oneironaut have said.

But looks need to be present for both initial interest and the ability to turn me on.