Thanks for this thread. I've got a few more books to add to my must read list.
For me, there's Elizabeth Bennett of course but also Sophie from Howl's moving castle, Momoko from Kamikaze Girls and Cimorene from Enchanted Forest Chronicles. Oh and Trinity from Matrix as well as Scully from X-files. [I'm probably going to curse myself for forgetting someone important but as it stands right now, this is my list. I think.]
I really like it when you feel like the characters have very distinct personalities, so Anna from Anna and the French Kiss, Rory Deveaux from The Shades of London, and Ruby Oliver. All of these characters have actual personalities and feel like actual characters as opposed to just being used as a person who's eyes we can view the story through.
In general It would have to be Yuki Nagato from the Haruhi Suzumiya series of anime and manga. She is mostly silent yet still incredibly compelling. Her character just becomes increasingly more complex as the series progresses and some how the empathy we feel for her as an audience makes the endless 8 make sense.