Burns is generally classified as a proto-Romantic poet, and he influenced William Wordsworth, Samuel Taylor Coleridge, and Percy Bysshe Shelley greatly. His direct literary influences in the use of Scots in poetry were Allan Ramsay and Robert Fergusson. The Edinburgh literati worked to sentimentalise Burns during his life and after his death, dismissing his education by calling him a "heaven-taught ploughman". Burns influenced later Scottish writers, especially Hugh MacDiarmid, who fought to dismantle what he felt had become a sentimental cult that dominated Scottish literature.
Burns had a significant influence on Alexander McLachlan and some influence on Robert Service. While this may not be so obvious in Service's English verse, which is Kiplingesque, it is more readily apparent in his Scots verse.
Scottish Canadians have embraced Robert Burns as a kind of patron poet and mark his birthday with festivities. 'Robbie Burns Day' is celebrated from Newfoundland and Labrador to Nanaimo. Every year, Canadian newspapers publish biographies of the poet, listings of local events and buffet menus. Universities mark the date in a range of ways: McMaster University library organized a special collection and Simon Fraser University's Centre for Scottish Studies organized a marathon reading of Burns' poetry). Senator Heath Macquarrie quipped of Canada's first Prime Minister that "While the lovable [Robbie] Burns went in for wine, women and song, his fellow Scot, John A. did not chase women and was not musical!"  'Gung Haggis Fat Choy' is a hybrid of Chinese New Year and Robbie Burns Day, celebrated in Vancouver since the late 1990s.
In January 1864, President Abraham Lincoln was invited to attend a Robert Burns celebration by Robert Crawford; and if unable to attend, send a toast. Lincoln composed a toast.
An example of Burns's literary influence in the U.S. is seen in the choice by novelist John Steinbeck of the title of his 1937 novel, Of Mice and Men, taken from a line in the second-to-last stanza of "To a Mouse": "The best laid schemes o' mice an' men / Gang aft agley." Burns's influence on American vernacular poets such as James Whitcomb Riley and Frank Lebby Stanton has been acknowledged by their biographers. When asked for the source of his greatest creative inspiration, singer songwriter Bob Dylan selected Burns's 1794 song "A Red, Red Rose" as the lyric that had the biggest effect on his life. The author J. D. Salinger used protagonist Holden Caulfield's misinterpretation of Burns's poem "Comin' Through the Rye" as his title and a main interpretation of Caulfield's grasping to his childhood in his 1951 novel The Catcher in the Rye. The poem, actually about a rendezvous, is thought by Caulfield to be about saving people from falling out of childhood.
Burns became the "people's poet" of Russia. In Imperial Russia Burns was translated into Russian and became a source of inspiration for the ordinary, oppressed Russian people. In Soviet Russia, he was elevated as the archetypal poet of the people. As a great admirer of the egalitarian ethos behind the American and French Revolutions who expressed his own egalitarianism in poems such as his "Birthday Ode for George Washington" or his "Is There for Honest Poverty" (commonly known as "A Man's a Man for a' that"), Burns was well placed for endorsement by the Communist regime as a "progressive" artist. A new translation of Burns begun in 1924 by Samuil Marshak proved enormously popular, selling over 600,000 copies. The USSR honoured Burns with a commemorative stamp in 1956. He remains popular in Russia after the fall of the Soviet Union.