A rolling stone gathers no moss is an old proverb, first credited to Publilius Syrus, who in his Sententiae states, People who are always moving, with no roots in one place or another, avoid responsibilities and cares. The phrase spawned a shorter mossless offshoot image, that of the rolling stone, and modern moral meanings have diverged, from similar themes such as used in the popular song "Papa Was a Rollin' Stone", to a more complementary commentary on "freedom" from excessive rootedness, such as in the band The Rolling Stones.
The saying may not be authentic to Publilius Syrus, as the Latin form usually given, Saxum volutum non obducitur musco, does not appear in his edited texts. It is first documented in Egbert of Liège collection in Latin "Fecunda Ratis" (The Well-Laden Ship), V. 182, of about 1023: "Assidue non saxa legunt volventia muscum." So the proverb was not invented but made popular 500 years later by Erasmus' Adagia, first published in England around 1500. He gave it in Greek and in Latin. It is also given as "Musco lapis volutus haud obducitur", and in some cases as "Musco lapis volutus haud obvolvitur".
The conventional English translation first appeared in John Heywood's collection of Proverbs in 1546, crediting Erasmus. Brewer's Dictionary of Phrase and Fable also credits Erasmus, and relates it to other Latin proverbs, Planta quae saepius transfertus non coalescit or Saepius plantata arbor fructum profert exiguum, which mean that a frequently replanted plant or tree yields less fruit than say an olive or oak tree that is left in place for hundreds of years. 
By the 19th century, the theme of "rootlessness having negative consequences" was still much in place. To quote the 1825 Dictionary of Scots Language: "Any gentleman, whether possessing property or not, who was popular, and ready to assist the poor in their difficulties, might expect a day in the moss, as they were wont to term it, and could have them longer for payment." At the time, "A day in the moss" referred to cutting peat in bogs (made of consolidated sphagnum moss). referring to hard work in preparation for winter. An itinerant "rolling stone" will not likely feel the timely need to "gather moss", by applying for access to a community's peat bog. 
The phrase was popular in England in the early 20th century. In Swallows and Amazons, published in 1930 by the English children's author Arthur Ransome, the theft and eventual return of "Captain Flint's" memoirs Mixed Moss by A Rolling Stone, forms an important narrative in the story.
By the 1940s, in The Return of the King by J.R.R. Tolkien, Gandalf tells the hobbits that Tom Bombadil “...is a moss-gatherer, and I have been a stone doomed to rolling. But my rolling days are ending, and now we shall have much to say to one another.” Though the two are both ancient figures, Gandalf has remained involved throughout history, until here where his story is beginning to recede from the realms of men.
In The Rolling Stones, a 1952 novel by science fiction author Robert A. Heinlein, a family travels throughout the Solar System looking for adventure and money. Hazel Stone, the grandmother, justifies the initiation of their rootless existence saying: "this city life is getting us covered with moss", when they buy their ship, with the theme carrying throughout the book.
Union activist Joe Hill's last will, written in the form of a song in 1915, states: "My kin don't need to fuss and moan / Moss does not cling to rolling stone." Hank Williams's "Lost Highway" opened with the line "I'm a rolling stone/All alone and lost", inspiring later songs to use the rolling stone metaphor, many of which dropped the reference to moss.
"Rollin' Stone" is a 1950 song recorded by blues legend Muddy Waters, which inspired the band name The Rolling Stones, and the 1965 song "Like a Rolling Stone" by Bob Dylan, which in turn inspired the magazine Rolling Stone. 
The Temptations released the song "Papa Was a Rollin' Stone" in 1971. Don McLean's 1970s "American Pie" reprised a reference to moss, with "Now for ten years we've been on our own / And moss grows fat on a rollin' stone". "Flames", a song by ZAYN, R3HAB and Jungleboi contains the line "'Cause I'm a rolling stone / And I keep rolling on".
Because it is so well known, this saying is one of the most common proverbs used in psychological tests for mental illness. American psychiatric research  conducted in the 1950s between control groups of healthy Air Force personnel against hospitalized Veterans Administration patients with schizophrenia found that the lack of abstraction ability was statistically higher in the VA patients. This led researchers to believe that persons with mental illness were only capable of "concrete" thinking, or interpreting metaphorical or abstract concepts literally, often simply restating the proverb in different words. 
Ken Kesey, who had participated in Air Force mental health studies using LSD, derided what he felt were the simplistic conclusions of these psychiatrists in his book One Flew Over the Cuckoo's Nest, in a scene where a psychologist asks McMurphy what he thinks the proverb means. After an initial smart-aleck response, McMurphy says he guesses it means, "It's hard for something to grow on something that's moving." McMurphy is forced to submit to a lobotomy at the end of the story, partially "justified" by the perceived "pathology" indicated by his "concrete" response.
The research results have, in practice, often been improperly generalized to suggest a lack of metaphorical understanding of proverbs alone can be an indicator of mental illness.
In film and TVEdit
The 1975 film One Flew Over the Cuckoo's Nest included the book's scene with McMurphy ridiculing the psychologist. In 2005 the television show MythBusters rolled a stone constantly for six months, and did not measure any moss growth during that time. 
One of the limousines says the proverb in the last scene of Leos Carax's Holy Motors (2012).
- Adagia, Erasmus, at Bibliotheca Augustana.
- Jerónimo Martín Caro y Cejudo, Refranes, y modos de hablar castellanos (1792), p. 288 
- Brewer's Dictionary of Phrase and Fable Archived October 26, 2006, at the Wayback Machine, sub. title "Rolling Stone".
- "A day in the moss".
- Dictionary of the Scots Language Sc. 1825 J. Mitchell Scotsman's Library 118: "Any gentleman, whether possessing property or not, who was popular, and ready to assist the poor in their difficulties, might expect a day in the moss, as they were wont to term it, and could have them longer for payment." http://www.dsl.ac.uk/entry/snd/moss
- "The Death of Joe Hill". The New York Times. Retrieved March 16, 2018.
- "Coverwall". Rolling Stone.
- Clinical Manual for Proverbs Test, 1956, Dr Gorham, Missoula MT., Psychological Test Specialists
- "Proverb interpretation in forensic evaluations", William H. CampbellMD, MBA and A. Jocelyn RitchieJD, PhD, AAPL Newsletter, American Academy of Psychiatry and the Law, Jan 2002 Vol. 27 No. 1, pp. 24-27
-  Annotated MythBusters
- "George Herriman".