This article is from the alt.usage.english FAQ, by Mark Israel email@example.com with numerous contributions by others.
Genesis 10:8-9, in describing how the Seventy Nations were
founded by the descendants of Noah, says that Nimrod, son of Cush,
son of Ham, son of Noah, was "a mighty man on earth" and "a mighty
hunter before the LORD". The word "nimrod" is recorded in English
since 1545 with the (now obsolete) meaning "tyrant", and since
1712 with the meaning "hunter".
In contemporary U.S. slang, "nimrod" means "fool, numbskull".
Rex Knepp ingeniously suggested that the origin of this was Bugs
Bunny's taunt of Elmer Fudd: "So long, Nimrod." Unfortunately for
this theory, Jesse Sheidlower says that Random House has two
citations of "nimrod" = "numbskull" from the 1930s, before the Bugs
Bunny episode containing the taunt.