Anything Goes is a tuneful ocean crossing on the S.S. America. Billy Crocker comes to the ship for instructions from his Wall Street boss, E. J. Whitney. While there he discovers that the love of his life, Hope Harcourt (chaperoned by her mother) and her fiancé, Lord Evelyn Oakleigh, are on board. Also on board is dance-hall sweetheart Reno Sweeny and her chorus girls.

Billy decides to stow away and somehow win Hope. He runs into public enemy No. 13 Moonface Martin (disguised as a minister of religion) and his moll, Erma. Moon has an extra ticket intended for Public Enemy No. 1, Snake Eyes Johnson, who has failed to show up for the crossing. Someone on board suggests that Billy is Public Enemy No. 1, and the chase is on.

Incorporating various disguises, Billy continues to woo Hope. Back on shore the real No. 1 is captured in the company of the real minister, but Billy and Moon do not get the message and escape from the brig, where they have been placed for their suspicious actions.

Like all 1930s musicals the end is utopian with Billy getting Hope, Reno gets Sir Evelyn, E. J. Whitney gets Mrs. Harcourt. Moon gets a pardon and is free to express openly his love for Erma.