I'm not picking just one either, since every character that has managed to become a favourite, has for different reasons, and from different genres.

Jane Eyre. What a strong character in an interesting classic, and all without being a super hero or badarse.
Puddleglum, from "The Silver Chair" of the Chronicles Of Narnia series. Comically pessimistic, he has a good head for navigating through some pretty perilous situations, and never sells himself out and gives way to the wrong side, even when it is the most popular/persuasive to others. He isn't fooled by characters trying to pretend to be something other than what they are, either.
Misery Chastain "Misery" She's got a couple of cool things going for her. She's a character within a fictional book, within a fictional book. She's got a very unlikely name, and that makes rping her as a pleasant person pretty fun. She has the unlikely name thing in common with Fortunato from that dreadful short story "Mateo Falcone" whose title character I detest.
Robert Goren from "Law And Order CI" just awesome. Detective and near genius all wrapped up in one.
Jessica Fletcher "Murder She Wrote" How she can get at the truth, often without people realizing she is on to them, and how she keeps her cool under all kinds of situations, just wow.
Gretel from the story "Hansel And Gretel" This is no damsel in distress. She wasn't afraid to act when she saw the only way she could save herself and her brother. and what had to be done wasn't pretty, but it was necessary. she is kickbutt. also, doing one of those "Which fairy-tale character are you?" type quizzes a long time ago, this was my result. Cool. Fun to rp.
Spider Man. Well, who doesn't like Spider Man? Everyone knows who he is, and I mention the old cartoon in another thread. Good watching when you just want to chill.
Pippi Longstocking - everybody's heard of her, too. Favourite character in a one of my favourite books growing up. Even as a little girl, she didn't let anyone push her around, and stood up for what was right. She did a few super heroism things, some of which could land her in Sue territory if they didn't occur in a fun fiction book that is friendly for all ages. I wished I had a friend like her. I wished I could have quite a few of the things she had. The super hero quality she has is unusual physical strength, which she seems to be most famous for.
But as an rp character, I had to re-make her to an adult version, since no one would take a little girl seriously. With that came giving her an adult mind and personality. I kept the physical strength and her Fletcher/Gorenesque way of keeping cool and figuring things out. This also made her the most challenging character to write, particularly when some other rp character that said/wrote something to her was really odious, But adult Pippi is far more diplomatic than I am, so much as I wanted to tell some character they sucked, I couldn't do that when having to respond as Pippi. She really schooled me on how to deal with difficult people without blowing my top.