When JK Rowling outed Dumbledore my first thought was that I would never do anything like that, because if a character of mine isn't gay on the page, then he isn't gay, period. I know very little about them that's not written down. I don't make up elaborate backstories. Usually I know a detail or two that's not explicitly in the text, but it's all vague and subject to change, and if it doesn't change it probably will end up in the text at some point. Just recently a character surprised me by having sex with another woman. I had no idea she was into that, but in hindsight it explains a lot about her.
How about you? Do you know more about your characters than your readers do? To expand on the subject, if there's something left vague, unanswered, implicit or mysterious in a story, do you always know the answer?