Apple support around the world has acknowledged the issue of "redeemed" codes being sent out for free Mountain Lion upgrades from the App Store, according to users on several message boards right now.
The Internet nearly exploded with news of Apple's release of OS X 10.8 Mountain Lion less than an hour ago.
When I received an App Store redeem code for a Mountain Lion upgrade just after release, I tried to use it and the App Store said that the code had been redeemed. Apple is giving free upgrade codes to customers who have purchased Macs after June 11, 2012 if they apply for an Up-to-Date claim here.
Looking at many message board communities, it appears that Apple is working on a fix and may be sending out new codes to these customers shortly.
Cult of Mac says that one of their readers has been advised to try in a hour, when the problem may have been fixed.
UPDATE:
Compiling information from various sources around the web and message boards, here's the deal:
Apple accidentally opened up the Up-to-Date form early and issued legit codes to many people. When they said "oops" and closed it back again, it reset the code banks. When they opened it up again after the release, they were issuing used codes.
They are now going to send affected users new codes (which may take hours to a couple days). Some people have already got new codes, while others (like me) are waiting.
Moreover, people who apply for the code now will not get an immediate email like the ones who applied early. They will get codes when everybody gets codes.
Another UPDATE:
I got my second code in an identical set of emails from Apple about 30 hours after I got the initial one that didn't work. It did not require any work on my side.