IMO, wrapping exceptions (checked or otherwise) has several benefits that are worth the cost:
1) It encourages you to think about the failure modes for the code you write. Basically, you have to consider the exceptions that the code you call may throw, and in turn you'll consider the exceptions you'll throw for the code that calls yours.
2) It gives you the opportunity to add additional debugging information into the exception chain. For instance, if you have a method that throws an exception on a duplicate username, you might wrap that exception with one that includes additional information about the circumstances of the failure (for example, the IP of the request that provided the dupe username) that wasn't available to the lower-level code. The cookie trail of exceptions may help you debug a complex problem (it certainly has for me).
3) It lets you become implementation-independent from the lower level code. If you're wrapping exceptions and need to swap out Hibernate for some other ORM, you only have to change your Hibernate-handling code. All the other layers of code will still be successfully using the wrapped exceptions and will interpret them in the same way, even though the underlying circumstances have changed. Note that this applies even if Hibernate changes in some way (ex: they switch exceptions in a new version); it's not just for wholesale technology replacement.
4) It encourages you use different classes of exceptions to represent different situations. For example, you may have a DuplicateUsernameException when the user tries to reuse a username, and a DatabaseFailureException when you can't check for dupe usernames due to a broken DB connection. This, in turn, lets you answer your question ("how do I recover?") in flexible and powerful ways. If you get a DuplicateUsernameException, you may decide to suggest a different username to the user. If you get a DatabaseFailureException, you may let it bubble up to the point where it displays a "down for maintenance" page to the user and send off a notification email to you. Once you have custom exceptions, you have customizeable responses -- and that's a good thing.