Anything Goes begins late at night in a smoky Manhattan bar. Billy Crocker (Howard McGillin), a handsome stockbrokers' assistant, has forgotten his date with Reno Sweeney (Patti LuPone), the sexy evangelist-turned-nightclub singer. He explains that he's been running errands for his boss, Elisha J. Whitney (Rex Everhart), who is sailing to London in the morning. Reno, who is sailing on the same ship as Whitney, forgives Billy and invites him to sail with her – "I Get a Kick Out of You." Billy declines – he's in love with another woman and must remain in New York to pursue her.

The next morning. The luxury liner S.S. American is preparing to sail. Reporters complain to the chagrined Captain about the lack of celebrities among the arriving passengers: no note-worthies, except the notorious Reno Sweeney. They brighten at the entrance of the famed debutante Hope Harcourt (Kathleen Mahony-Bennett). Hope is accompanied by her widowed mother, Evangeline (Anne Francine), and by a wealthy Englishman, Lord Evelyn Oakleigh (Anthony Heald), whom she announces she will marry aboard ship.

Billy arrives to see Mr. Whitney off – but then he spots Hope, the woman he loves. He decides to stow away, so he can convince Hope to marry him instead of Lord Evelyn. There are two other stowaways on board: Moonface Martin (Bill McCutcheon), a second-rate gangster disguised as a minister, and Erma (Linda Hart), the girlfriend of his partner-in-crime, "Snake Eyes" Johnson – Public Enemy #1. The "all ashore" is called; "Snake Eyes" has missed the boat. Erma gives Billy his phony passport and ticket. The ship pulls out to sea with the passengers and crew singing "There's No Cure Like Travel"/"Bon Voyage."

That evening Reno discovers Billy on deck and learns that the woman Billy's in love with is on the ship, too. But she doesn't hold that against him. In fact, when Billy admits that a debutante like Hope may be out of his league, Reno gives him a pep talk – "You're the Top." Feeling braver, Billy seeks out Hope, who is both thrilled and horrified to find him on board. She insists she has to marry Lord Evelyn; he insists she's going to marry him – "Easy To Love." Meanwhile, Mr. Whitney has developed an amorous interest in Hope's mother. In his cabin he prepares for what he hopes will be a romantic tryst – "I Want To Row on the Crew."

The next morning four crew members entertain the passengers on deck – "Sailors' Chantey." The Captain, having learned that Public Enemy #1 is hiding on board, instructs his sailors to ferret out this "master of disguise." Billy, however, is wearing an ill-fitting sailor suit that fools no one. Reno recognizes him immediately and also sees through Moonface's minister get-up. Old friends, Reno and Moonface work out a plan to help Billy get Hope: Reno will vamp Lord Evelyn and Moonface will blackmail him into breaking the engagement. Moonface tells Reno they should have teamed up years ago. She agrees – after all, they're two of a kind – "Friendship."

The plan to blackmail Lord Evelyn backfires.

Reno decides that "Evie" is "kinda cute" and can't go through with the caper. Moonface and Billy adopt new disguises and try to convince Hope's mother that Lord Evelyn is really a deranged impostor, escaped from Bedlam. This scheme also fails, when Hope exposes Billy, who exits, pursued by sailors. Billy, undaunted, sneaks back to romance Hope ("It's De-Lovely"), and this time she melts. Unfortunately, having abandoned his disguise, Billy is set upon by crew members. They've finally caught Public Enemy Number One! Rather than clap him in irons, however, the Captain – ever eager to satisfy the passengers' hunger for celebrities – makes Billy the honorary captain of the ship. Reno, noting how "times have changed," leads the company in a rousing, tap-filled – "Anything Goes."

That evening at the Captain's table Billy and Moonface are serenaded by the passengers and crew – "Public Enemy Number One." Dinner is followed by one of Reno's sensuous "sermons" ("Blow, Gabriel. Blow"), during which all the passengers confess their sins, including Lord Evelyn, who admits to a "romp in the rice" with a certain "Little Plum Blossom" when he visited China some years ago. Billy confesses too: he's not really the famous criminal they all thought he was. The crowd immediately turns on him, and he and Moonface are dragged off to the brig. Hope finally admits to herself that she's in love with Billy – too late – "Goodbye, Little Dream, Goodbye."

In the ship's brig Moonface tries to cheer Billy up – "Be Like the Bluebird." Billy is unmoved, until Erma arrives with a note from his beloved: "Dearest darling, I love you so, but what good does love do when there is no hope? Love, Hope." Billy knows then that things will work out somehow – "All Through the Night." Meanwhile, on deck, Reno encounters Lord Evelyn, who is composing a poem to his beloved. He confides to Reno that he's fallen for her, but that his family's code of honor requires that he make good on his promise to marry Hope. When Reno questions how his "romp in the rice" fits in with the Oakleigh code, he discloses a deep, dark secret – "The Gypsy in Me."

The morning of the wedding. A bunch of love-struck sailors surround Erma, imploring: "We're going to have one wedding, why not two?" Erma wonders if they've considered what married life with her would be like – "Buddie, Beware." Finally, the big moment arrives, and all are assembled for the wedding. Billy and Moonface - who've escaped from the brig dressed as Chinese – interrupt the ceremony to insist that Lord Evelyn make an honest woman of little Plum Blossom (actually Reno, in a Chinese robe). In a triply happy ending, Hope marries Billy, Reno marries Lord Evelyn, and Hope's mother marries Mr. Whitney – "I Get a Kick Out of You"/"Anything Goes" (reprises).