Only three New York mayors were ever re-elected twice -- Fiorello LaGuardia and Robert Wagner were the others -- and all three left office, as The New York Times put it in 2008, "drained, diminished and disdained."
Some new Yorkers thought Koch, who published an autobiography in 1984, had lost control of his ego.
Koch even said he lost because "voters got tired of me."
Koch, who never married, was often criticized by playwright, novelist and LGBT rights advocate Larry Kramer for not doing more to stop the spread of AIDS in New York.
"He was a closeted gay man, and he did not want in any way to be associated with this," Kramer declared to New York magazine.
Koch found discussions of his sexuality to be humorous.
"Listen, there's no question that some New Yorkers think I'm gay, and voted for me nevertheless. The vast majority don't care, and others don't think I am. And I don't give a (expletive) either way!" he told New York magazine.
There will be a funeral on Monday.