“Never Again Volunteer Yourself” is a backronym (back acronym) of the word “navy” that has been printed on several gift items, such as bumper stickers, T-shirts and posters. “Never Again Volunteer Yourself” has been cited in print since at least 1990 and is of unknown authorship.
 
 
5 September 1990, The News (Frederick, MD), “Letters to the Editor,” pg. A6, col. 3:
When things weren’t going well, we used to say that “Navy” stood for “Never Again Volunteer Yourself.”
(William P. Kirk, Frederick—ed.)
 
Google Books
Duck and Cover:
A Novel
By Brenda Peterson
New York, NY: HarperCollins Publishers
1991
Pg. 161:
On the base, all the other navy wives kept Mathilde in line; but in the city, Mathilde got the notion that the navy was a four-letter word for Never Again Volunteer Yourself.
 
Google Books
How to Connect
By Chris Shipley
Emeryville, CA: Ziff-Davis Press
1993
Pg. 27:
NAVY— never again volunteer yourself
 
Google Books
Acronymania:
A Celebratory Roundup of Nomenclature Yielding Mischief:
Abbreviations, Neologisms, Initialisms, Acronyms!
By Don Hauptman
New York, NY: Dell Pub.
1993
Pg. 224:
Navy means “Never again volunteer yourself.”
 
Google Books
The Deception
By Esther Smith
Bloomington, IN: AuthorHouse
2006
Pg. 37:
I didn’t find out what the word “Navy” meant until some people were joking one day and this guy told me that it meant, “NEVER AGAIN VOLUNTEER YOURSELF”.
 
Google Books
Drawn to Injustice:
The Wrongful Conviction of Timothy Masters
By Timothy Masters and Steve Lehto
New York, NY: Bekley Publishing Group
2012
Pg. ?:
I had been told by many people to never volunteer for anything in the Navy. One common joke I heard was that Navy stood for “Never Again Volunteer Yourself.”