“Two peanuts were walking down the street—one was assaulted” (“assaulted” is a pun on “a salted” peanut) is a joke that has been published on many websites. “Two peanuts were walking down the street and one was assaulted (a salted)” has been cited in print since at least 1953.
 
There are New York and Central Park versions:
 
. “Two peanuts were walking through the New York. One was assaulted.”
. “Two peanuts were walking in Central Park. One was assaulted.”
 
“Two peanuts walk into a bar…” is a bar joke version.
     
 
Wikipedia: The Funniest Joke in the World
“The Funniest Joke in the World” is the title most frequently used for written references to a Monty Python’s Flying Circus comedy sketch, which is also known by two other phrases that appear within it, “Joke Warfare” and “Killer Joke”, the latter being the most commonly spoken title used to refer to it. The premise of the sketch is that the joke is so funny that anyone who reads or hears it promptly dies from laughter.
 
Broadcast
The sketch appeared in the first episode of the television show Monty Python’s Flying Circus (“Whither Canada”), first shown on October 5, 1969.
(...)
The Germans attempt counter-jokes. Eventually their best joke is used in action (“Der ver zwei peanuts, valking down der strasse, and von vas . . . assaulted! peanut.”), but proves in English to be ineffective.
   
Pithypedia
Two peanuts were walking through the New York. One was assaulted.
—Anonymous
   
Newspapers.com
16 December 1953, Los Angeles (CA) Times, “Cityside” with Gene Sherman, pt. 1, pg. 2, col. 1:
Two peanuts went for a walk through a particularly rough section of town, muses H.S.W. fancifully. One was a salted.
 
Newspapers.com
5 March 1954, Daily News (Los Angeles, CA), Matt Weinstock column, pg. 6, col. 6:
There is also a character running around loose who asks if you’ve heard about the two peanuts walking down the street. One was a salted.
 
Newspapers.com
29 March 1954, Calgary (Alberta) Herald, “Furrows and Foothills” by Ken Liddell, pg. 3, col. 5:
Heard a joke: Two peanuts went for a walk in the woods; one was a salted. Not much of a joke.
 
Newspapers.com
7 September 1958, Denton (TX) Record-Chronicle, “High School News” by David Robinson, sec. 2, pg. 6, col. 1:
I interrupt this summary to give you a news bulletin. Last night two peanuts were walking down the street and one was a-salted!
 
21 November 1958, Indiana (PA) Evening Gazette, “Inside Indiana” by Bill Hastings, pg. 1, col. 1:
It didn’t originate here: “Two peanuts went for a walk in the woods. One was a salted,” so says Mo Mabon.
 
1 November 1980, Daily Northwestern (Evanston, IL),  TGIF, pg. 12, col. 1:
Two peanuts were walking down the street and one was assaulted.
 
Google Books
When You’re Up to Your Ass in Alligators: More Urban Folklore from the Paperwork Empire
By Alan Dundes and Carl R. Pagter
Detroit, MI: Wayne State University Press
1987
Pg. 217:
The two peanuts that took a walk in the woods — one was assaulted?
 
5 March 1987, Augusta (GA) Chronicle, ‘Perlman forced to become connoisseur” by John Rockwell (New York Times), pg. 2, col. 3:
As he puttered away, Perlman cracked terrible food jokes (“Two peanuts were walking in Central Park; one was assaulted”) and dropped cooking hints that a neophyte food writer dutifully jotted down.
(Itzhak Perlman—ed.)
 
Google Books
The Book of Words
By Lawrence Kushner
Woodstock, VT: Jewish Lights Pub.
1993
Pg. 66:
Two peanuts were walking down the street. One was assaulted…peanut.
 
Google News Archive
4 February 1993, Madison (IN) Courier, “I’m Just Sayin’” by Scott Karst, pg. 9, col. 1:
That was probably the dumbest thing I ever heard in my 28 1/2 years on this planet, with the one exception being my uncle’s joke about two peanuts walking down the street and one was assaulted (a salted).
 
The Canonical List of Taglines 
Maintained by Jascha Franklin-Hodge .(JavaScript must be enabled to view this email address)
Last Update: 1994/11/27 5:22pm EST
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Two peanuts went to New York. One was assaulted.
 
23 September 1996, Rocky Mountain News (Denver, CO), “The Monday Joke” by Rebecca Jones:
Two peanuts were walking in Central Park, one was assaulted.
   
Google Books
The Best Life List:
Your Itemized Guide to the Good Life
By Dee Dee Clermont
Avon, MA: Adams Media
2012
Pg. 142:
Word-Play Joke: Two peanuts were walking down the street. One was assaulted.