A couple years ago a vBulletin modification came out allowing admins to view the PM's of members. Obviously, the discussion ensued regarding whether this was ethical/lawful, etc. but that aside, the modification nevertheless exists for all vBulletin license holders. However, this modification is for an older version of vBulletin than this forum uses, which means it may not be a compatible modification even if someone were to try and install it here. For the record I trust the mods and admins on this site and think they do a fantastic job. This discussion is all simply theoretical.This forum is running vbulletin. Ask the company that makes it this question.
Apart from that, the only way a mod or admin could view your private messages would be to change the password of a user's account in the Admin Control Panel. They could then log into that user's account using the newly changed password and view the PM's. The user, however, would not be able to log back in as the admin/mod cannot change the password back to what it was (because they wouldn't know what it was, only what they've changed it to).