I knew a guy at Dartmouth College who got the appropriate certifications to perform marriages in Vermont. (He married a couple of grad students that I know of.)
After reading the statutes and procedures, he used to claim that if you wanted, he could successfully marry you to your cat. His definition of success included filing all necessary paperwork and receiving an official marriage license from the State of Vermont. It did not include standing up to any possible court case later.
He was somewhat disappointed that he couldn't find anyone who wanted to test his theory out by actually marrying their cat... (I can still remember him saying, "Well if you don't like cats, what about your dog? I do dogs as well!")
Cheers,
Ben