mid-15c., Scottish gouf, usually taken as an alteration of Middle Dutch colf, colve "stick, club, bat," from Proto-Germanic *kulth- (source also of Old Norse kolfr "clapper of a bell," German Kolben "mace, club, butt-end of a gun"). The game is from 14c., the word is first mentioned (along with fut-bol) in a 1457 Scottish statute on forbidden games (a later ordinance decrees, "That in na place of the realme thair be vsit fut-ballis, golf, or vther sic unprofitabill sportis" [Acts James IV, 1491, c.53]). Despite what you read on the internet, "golf" is not an acronym (this story seems to date back no earlier than 1997). Golf ball attested from 1540s; the motorized golf-cart from 1951. Golf widow is from 1890.
Oh! who a golfer's bride would be,
Fast mated with a laddie
Who every day goes out to tee
And with him takes the caddie.
["The Golf Widow's Lament," in Golf magazine, Oct. 31, 1890]
c. 1200, from Old English gamen "joy, fun; game, amusement," common Germanic (cognates: Old Frisian game "joy, glee," Old Norse gaman "game, sport; pleasure, amusement," Old Saxon gaman, Old High German gaman "sport, merriment," Danish gamen, Swedish gamman "merriment"), said to be identical with Gothic gaman "participation, communion," from Proto-Germanic *ga- collective prefix + *mann "person," giving a sense of "people together."
The -en was lost perhaps through being mistaken for a suffix. Meaning "contest for success or superiority played according to rules" is first attested c. 1200 (of athletic contests, chess, backgammon). Especially "the sport of hunting, fishing, hawking, or fowling" (c. 1300), thus "wild animals caught for sport" (c. 1300), which is the game in fair game (see under fair (adj.)), also gamey. Meaning "number of points required to win a game" is from 1830. Game plan is 1941, from U.S. football; game show first attested 1961.
"a winning of all tricks in a card game," 1660s, earlier the name of a card game (also called ruff), 1620s, used especially in whist, of obscure origin. Grand slam in bridge is recorded by 1892; earlier in related card games by 1800; figurative sense of "complete success" is attested by 1920; the baseball sense of "home run with the bases loaded" is by 1935, probably a natural extension from the card game sense, with suggestion of slam (n.1). It also was the name of a brand of golf clubs in the 1920s and '30s.