“Marriage is a great/wonderful institution, but who wants to live in an institution?” is a classic joke about marriage. “Marriage is a great institution; but who wants to live in an institution?” was said (and probably originated) by the actor Raymond Hitchcock (1865-1929) in the play Betty (1916).
 
Both New York City-born comedian and actor Groucho Marx (1890-1977) and Brooklyn-born actress Mae West (1893-1980) have been credited with the famous line, but there is no evidence to suggest that either originated it.
     
 
Wikipedia: Raymond Hitchcock (actor)
Raymond Hitchcock (October 22, 1865 – November 24, 1929) was a silent film actor, stage actor, and stage producer, who appeared in, or produced 30 plays on Broadway from 1898 to 1928, and who appeared in the silent films of the 1920s.
 
26 November 1916, Boston (MA) Sunday Post, “Under the Spotlight” by Edward Harold Crosby, Dramatic Page (pg. 38?):
For instance, he (Raymond Hitchcock in “Betty”—ed.) remarks: “They say marriage is an institution, but who wants to live in an institution?”
 
28 November 1916, Boston (MA) Post, “‘Betty’ Full of Girls: Hitchcock Comes to Tremont in English Play,” pg. 6, col. 3:
Just a specimen of his repartee: “Marriage? Marriage is a great institution; but who wants to live in an institution?”
 
Chronicling America
26 May 1917, The Labor Advocate (Cincinnati, OH), pg. 4, col. 2:
Well, After That—What?
Admitting that marriage is a great institution—who wants to live in an institution?
 
15 May 1920, The Morning Oregonian (Portland, OR), pg. 4, col. 3:
MINSTREL REMEMBERS GAME
PLAYED HERE 44 YEARS AGO
George Wilson, Now at Heilig, Recalls Contest With Firemen, With Keg of Beer as Prize for Winners
BY LEONE CASS BAER.
(...)
“I make a great tirade against married life; I poke fun at the institution of marriage, asking what sober man wants to live in an institution.”
(...)
Artist Happily Married.
“I am telling you this because I want to tell you also that no man in the world is more happily married than I am, and nothing I say in my monologue is applicable in my own case. For 27 years I have been married to the same wife, a sweet little woman who is back in our home in Binghamton, New York, and whose letters I read with as much joy as I did when she wrote her first ones to me.”
 
Google Books
Proceedings of the international conference of women physicians, Volume 3
New York, NY: Womans Press
1920
Pg. 94:
There occurs to me at this point a witty remark by one of our comedians. Some one says to him, “Isn’t marriage a wonderful institution?” The reply was,“Yes, but who wants to live in an institution?” (Laughter.)
   
1 November 1921, Trenton (NJ) Evening Times, “Names Brother in Suing for Divorce,” pg. 13, col. 2:
At other points in the diary Mrs. Ferrotta aphorizes as follows:
(...)
“Admitting that marriage is a great institution—who wants to live in an institution?”
 
Chronicling America
9 February 1922, The Seattle Star (Seattle, WA), pg. 1, col. 1:
LI’L GEE GEE, THE OFFICE VAMP, SEZ:
Admitting that marriage is a great institution, who wants to live in an institution?
 
Google News Archive
7 October 1954, Ocala (FL) Star-Banner, “Hollywood Needs A New Type Of Marriage” by Hal Boyle, pg. 12, col. 6:
Mae West once observed, reviving a joke older than the bustle: “Marriage is a great institution—but who wants to live in an institution?”
 
Google Books
The Modern Handbook of Humor
By Ralph Louis Woods
New York, NY: McGraw-Hill
1967
Pg. 287:
Marriage is a great institution — but who wants to live in an institution?
 
Google Books
And I Quote:
The Definitive Collection of Quotes, Sayings, and Jokes for the Contemporary Speechmaker
By Ashton Applewhite, William R. Evans III and Andrew Frothingham
New York, NY: St. Martin’s Press
1992
Pg. 382:
Marriage is a wonderful institution, but who wants to live in an institution? — Groucho Marx