Ssshhhh...

Typically when a game begins the heroes address each other and introduce themselves. Sometimes players divulge everything these is to know, where they come from, their hopes and dreams. Sometimes players have short divulges, "my character's name is bob, and he likes to fix things."

Almost never do players refuse to share something about their characters, nor do they lie. But, having a secret would be a great element to role-play with.

I've tossed around the idea before and never use it enough, but I encourage you to have a secret character sheet. Anything about your character that would be too embarrassing or damaging to make public can go on this secret character sheet. Throughout game play the other character can find clues and learn more about you. They may have known that Bob was an auto-mechanic, but they may never have known he was deep in debt.

Talk to your GM before you make any big secrets for your character. But, you could make a whole adventure around players finding out each others dirty secrets. Try and it out, and tell me how it goes.

Or maybe, don't tell me. Hush-Hush and all that.