"We don't make any formal promise about secrecy, but we don't plan to let anyone outside Y Combinator see these applications, including other startups we fund."
I think it's wise to trust the YC partners not to do anything intentionally nefarious, but to assume the worst of their unconscious minds.
When smart people read hundreds of ideas its got to cause a huge swarm in their heads. Most of the ideas get immediately buried in the unconscious. There's a definite chance a YC applicant's idea could eventually emerge and find its way in into a YC-funded company, in some form.
I definitely don't think this is a reason to not submit your application though. Everyone is going to know your idea after you launch anyway. If secrecy is your biggest asset you're in so much trouble this is a trivial concern.
/old
But seriously, ideas are totally worthless. I thought my totally awesome idea for a productivity site was worth a billion dollars too. And I built it and released it, and you know what? Nobody cared, and rightly so, because it was poorly executed. Now I'm playing catch-up with the design by making things cleaner, streamlined, and simple. That is what matters, not whatever your idea is. Though it's not until you've been steamrolled by brett and his clickable calendar that one can really understand that, maybe. :)
Bottomline: it is very difficult in this environment with start-ups launching left and right to claim ownership of a certain idea, even between two parties.
They certainly haven't launched a company doing what we wanted to do and no other YC company has, so you really don't need to worry about them stealing/sharing your idea. It's just not worth it for them.