There are a number of diseases and parasites that inflict zombie-like symptoms on their hosts, but only Cotard's Syndrome makes a person actually wholeheartedly believe they are the living dead.
Cotard's is a brain illness that stems from schizophrenia, and those afflicted believe that they are truly dead, actively putrefying or altogether non-existent. Some patients even feel that they have lost all their blood and vital internal organs.