Cotard's delusion is a rare mental disorder in which the sufferer is convinced that he or she is dead.

From Mind Hacks:

It's worth noting that although Cotard's delusion has come to represent 'the delusion that you're dead', Jules Cotard's original description (from 1880) was not actually that – it was a delusion of negation where the patient believed, as noted by Berrios and Luque, that she had "no brain, nerves, chest, or entrails, and was just skin and bone", that "neither God or the devil existed", and that she did not need food for "she was eternal and would live forever".