It used to be that you can crack passwords in the SAM registry file. In AD I'm not so sure that it would be that easy.
NT is specifically designed to NOT give you passwords. It stores them as hashes so the text isn't even available, and when users forget their password the admin can reset the password, not view the stored password. It also means that users know if someone's been goofing with their password because they would need to reset it or it's no longer what it was before.
So practically speaking, no, you can't retrieve passwords and there's no mechanism to do so. Technically speaking yes. You can mount a dictionary attack and hope there's no lockouts set in AD or you can try dumping account info with hacking tools and mount an offline brute force attack, and if your users had decent passwords, you might have your results in a couple days.
Side note-you might not WANT that ability anyway. In our organization, whoever has the password/account info is responsible for what's done in that account. We don't care if your friend was the one emailing that so and so looked hot in that skirt or that your buddy borrowed your account to visit hotandsweaty.com...you're on the hook if you have the account and you're not supposed to be sharing it. If you have that info then your users have plausible deniability that you have their password and could have been doing XYZ in their name, since all accounting stops at that account. But that's a policy question in your organization on how to handle it. We just would rather not deal with possible legal ramifications. NT preventing even admins from having that ability to view and catalog passwords is one of the few things I readily acknowledge that MS did right with their OS.