Joining the art department of True Detective magazine in 1932, he retouched photos of corpses for them. "A lot of those corpses were more interesting the way they were." Adams said of his work. He also did his first drawing for The New Yorker in that year. The Adams Family characters first appeared there in 1938 and continued until his death in 1988.
The Addams Family television series began with help from Addams himself in 1964. It only ran for 2 seasons, until 1966 but has, of course, enjoyed enduring popularity. The character of Morticia was based in part on his two wives, (known for his good looks and charm, he was also seen with Greta Garbo, Joan Fontaine and Jaqueline Kennedy). A friend of Alfred Hitchcock's, his art is referenced in North by Northwest.
For more info about him and the cartoon, check out the Unofficial Addams Family Cartoon website.