1809, American English, from dough + nut (n.), probably on the notion of being a small round lump (the holes came later, first mentioned c.1861). First recorded by Washington Irving, who described them as "balls of sweetened dough, fried in hog's fat, and called doughnuts, or olykoeks." Earlier name for it was dough-boy (1680s). Bartlett (1848) meanwhile lists doughnuts and crullers among the types of olycokes, a word he derives from Dutch olikoek, literally "oil-cake," to indicate a cake fried in lard.
Meaning "a driving in tight circles" is U.S. slang, 1981. Cf. also donut.