I can't really see past the classics so for me it would be Batman or Spiderman depending on when you asked me. I love the humour of some Spiderman material (mainly comics), but I also love the slightly more complex origin and scenarios you get in Batman material. Both of them have had film series I enjoyed as well (TDK trilogy and the Tobey Maguire Spider-Man films) which is good as I struggle to enjoy many superhero film series.
Outside of very obvious choices such as those, I would have to go with Batgirl. Obviously she isn't exactly unknown or anything, but at least it is slightly less obvious than the other two. I was especially enjoying her run in the New 52, but I wasn't too fussed after her reinvention last year.
If I read more comics then I am sure there is a possibility I would find a much more interesting character, but as it is I only have those.