I would never feel right reading them while my application is still being processed, or even after an interview, though I have a great relationship with my PI and she wouldn't mind at all. My two professors would, I believe, however.
However, I have read at several sites (UPenn-BGS comes to mind as a definite) that once matriculated, we have access to our files even if we waived our rights - I'm assuming that's so because you are no longer an applicant but a student of a particular university.
As a curious person, I actually probably would look at them then, and only not to prevent potential tension between some letter writers who didn't write something as good as you had hoped, or they suggested they would.
Overall, once you're in, I see no reason why a student shouldn't be able to review their file, and I guess universities agree.