A popular riddle is:
 
Q: What has a head and a tail, but no body?
A: A coin.
 
The riddle was cited in print in 1918 and published in many newspapers in 1940.
 
 
10 March 1918, The Daily Nonpareil (Council Bluffs, IA), “The Mail Box,” pg. 16, col. 1:
What has a tail and a head, but no body?
(...)
ALMA MEYER.
Malvern, Ia.
 
24 March 1918, The Daily Nonpareil (Council Bluffs, IA), “The Mail Box,” pg. 15, col. 5:
I think the answer to Alma Meyer’s riddle is a penny. The riddle was, “What has a head and tail but no body?”
(...)
NELLIE FREY.
Clarinda, Ia.
 
Google News Archive
6 July 1940, Owosso (MI) Argus-Press, “Riddles,” pg. 3, col. 3:
What has a head and a tail, but no body?
A penny.
   
Old Fulton NY Postcards
6 July 1940, Citizen-Register (Ossining, NY), “Riddles,” pg. 10, col. 3:
What has a head and a tail, but no body?
A penny.
 
Google Books
Encyclopedia of Puzzles and Pastimes
By Clark Kinnaird
New York, NY: Grosset & Dunlap
1946
Pg. 367:
59. What has a head and a tail but no body?
A. A cent.
 
7 July 1948, The Idaho Sunday Statesman (Boise, ID), “Riddles,” pg. 23, col. 3:
What has a head and a tail, but no body?
 
Google Books
Mathematical Fun, Games and Puzzles
By Jack Frohlichstein
New York, NY: Dover Publications
1962
Pg. 100:
Any banker should know this one. What has a head and a tail but no body?
   
Google Books
July 1962, Boys’ Life, “Think and Grin,” pg. 62, col. 1:
Q. What has one head, one tail, but no body?
A. A coin. — Arthur Payson, New York, 28, N.Y.
 
26 December 1962, Austin (TX) Statesman, “Fun Time—The Riddle Box,” pg. 6, col. 5:
What has one head, one tail, but no body?
A coin.
     
Google Books
January 2009, Boys’ Life, “Think & Grin,” pg. 51, col. 2:
Nathaniel: What has a head and a tail, but no body?
Bob: What?
Nathaniel: A penny!
Nathaniel Coad, Burke, Va.
 
Twitter
Befferny
‏@TINYKINGDOMS
‘What has a head, a tail, and no body?’ ‘Bethany.’ well now Abigail. I would have guessed sperm. The answer was a coin.
4:15 PM - 9 May 2009
 
Google Books
The Bumper Book of Very Silly Jokes
By Macmillan Children’s Books
London: Macmillan Publishers Limited
2013
Pg. 33:
What has a head and a tail but no body?
A coin.
 
What has arms and legs but no head?
A chair.
 
Google Books
Best Ever Classroom Jokes:
Because some of us never grow up
By Mike Haskins
New York, NY: Pavilion Books
2015
Pg. ?:
What has a head and a tail but no body?
A coin.