He very nearly became the host of The Tonight Show rather than Johnny Carson. Instead, Woody replaced the vacancy left by Carson and McMahon on the TV show Who Do You Trust? And interestingly, prior to all this, he was a distinguished Marine Corps Jet fighter pilot during the Korean War.
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Listen to a couple of his jokes from his album Woody Woodbury Looks at Love and Life - typical off-color gags used in clubs back in the day; generally about booze and slight sexual innuendo. The album says "for frisky adults only", but definitely G rated by today's standards.
WFMU's Beware of Blog has an excellent article on the interesting career of Woodbury. I highly recommend you check it out.