There's no formal pledge of secrecy but you have their word that they won't share your app with anyone outside of YC - and that includes other YC startups. It says so on the first para of the app.
You should take that with a grain of salt. Sure, the YC crew will try to not share your ideas -- but they're humans, and after reading five hundred applications, I'm sure there are ideas which stick in their skulls but which they don't remember came from a YC application.
In the end, the same rules apply to YC as apply everywhere else: If you have something which absolutely MUST remain secret, don't tell anyone.
