This is one of the most famous quotes attributed to the late great comedian and entertainer Groucho Marx. Supposedly he said this during a taping of his quiz show You Bet Your Life that ran from 1950-1960 (it began on radio in 1947; in its final year it was simply called the Groucho Marx Show). However, it was not aired, considered too risque at the time. This is not surprising when considering the context of the quote:
A female contestant says she has twenty three children (in some versions of the story it's only seventeen).
"Why so many children?" Groucho asks.
"Well, I just love my husband!" the woman replies.
"Well, I love my cigar, but I take it out of my mouth once in a while!" replies Groucho.
Since it was cut, actual film of this supposedly does not exist. The raucous laughter from the studio audience that followed, however, was used by NBC whenever such a reaction was needed in a laugh track. Groucho went back and forth, confirming and denying he actually said it.
According to BrooksMarlin: "This actually happened, but back when the show was still on the radio. A Mrs. Story from Bakersfield, CA was on the show and had 19 kids."
A few others have suggested I check out snopes.com. There was a rather interesting article about the remark there. Check out the full address below, but basically even snopes could not completely verify or discount the event happening. The only physical evidence that exists is a show log that does in fact show a husband and wife, Mr. and Mrs. Story, being on the show and they did indeed have nineteen children and were considered to be the largest family in America at the time.
Sources: http://en.wikipedia.org/wiki/You_Bet_Your_Life
http://www.snopes.com/radiotv/tv/groucho.htm