Four versions of the libretto of Anything Goes exist the original 1934 libretto, the 1962 off-Broadway revival libretto, the 1987 revival libretto, and the 2011 revival libretto. The story has been revised, though all involve similar romantic complications aboard the SS American and feature the same major characters. The score has been altered, with some songs cut and others reassigned to different scenes and characters, and augmented with various Porter songs from other shows.

Act I
Billy Crocker, a young Wall Street broker, has fallen in love with a beautiful girl he met at a party and spent the evening within a taxi. His boss, Elisha J. Whitney, is preparing to make a business deal and is going to travel to London aboard the SS American. Evangelist turned nightclub singer Reno Sweeney will be traveling aboard the same ship. Billy sees Reno as a friend, but she obviously has feelings for him ("I Get A Kick Out of You"). Billy goes to the dock to say farewell to his boss and Reno ("Bon Voyage"), and glimpses the mysterious girl again. He learns that she is heiress Hope Harcourt and, escorted by her mother, Mrs. Harcourt, is on her way to England with her fiancé Lord Evelyn Oakleigh, a handsome but stuffy and hapless British nobleman. Billy stows away on the ship in hopes of winning Hope's heart. "Moonface" Martin, a second-rate gangster labeled "Public Enemy 13," and his girlfriend, Bonnie, have disguised themselves as a minister and a missionary and, innocently aided by Billy, board the ship under their assumed identities, stranding the ship's real chaplain back at the port. Moonface and Bonnie mistakenly leave behind their leader, "Snake Eyes" Johnson, Public Enemy 1.

To thank him, Bonnie and Moonface let Billy have Snake Eyes Johnson's passport and ticket without telling him to whom they belong. Billy cons Evelyn into leaving him alone with Hope, by convincing him he is very ill. When he goes to get some air, Billy and Hope meet again, and it turns out she has been unable to stop thinking about him as well ("All Through The Night"). Though Hope prefers Billy, she insists she must marry Evelyn, though she gives no reason. Unbeknownst to Billy, her family's company is in financial trouble and marriage to Evelyn would promote a merger and save it. The ship's crew gets a cable from New York saying that Public Enemy 1 is on board. Moonface admits his true identity to Billy and he and Bonnie conspire to disguise Billy as a crew member since he is now presumed to be Snake Eyes Johnson.

A quartet of lovelorn sailors comforts themselves with the thought of romance when they reach the shore ("There'll Always Be a Lady Fair"). On deck, Bonnie lures the sailors to her ("Where Are The Men?"), then steals the clothes of one of the men for Billy.

Hope discusses her impending marriage with Evelyn and discovers that he is not particularly pleased with the engagement either. Billy asks Reno to help separate Evelyn and Hope, and she agrees. Billy and Reno reaffirm their friendship, ("You're the Top"). Reno tries to charm Evelyn, she succeeds, and he invites her for a drink in his cabin. She and Moon plot that Moon should burst into the cabin and discover Reno half-naked in Evelyn's arms, providing sufficient reason for breaking off the engagement. However, when Moon breaks into the room, machine gun in tow, he instead sees Reno fully dressed and Evelyn nearly undressed. Moon tries to invent some indecent explanation for the situation, but Evelyn insists that he would be quite pleased by any rumor depicting him as a passionate lover, especially if Hope heard it. Moon admits that the plot has failed.

The crew discovers that Billy is not a sailor, and Moon and Reno create a new disguise for him from a stolen pair of trousers, a jacket taken from a drunken passenger, and a haircut from Mrs. Harcourt's Pomeranian and made into a beard. Reno tells Billy that Evelyn has kissed her, and she is sure she will be Lady Oakleigh soon since love moves so quickly these days ("Anything Goes"). Mrs. Harcourt, recognizing her dog's hair, angrily pulls off Billy's beard and the crew and passengers realize he must be the wanted man. As Snake Eyes Johnson, Billy is an instant celebrity.

Act II
Billy is honored by both crew and passengers as "Public Enemy Number One." He tells the Captain that Moon (who is still disguised as a minister) is helping him reform from his wicked ways. Moon is asked to lead a revival in the ship's lounge. The passengers confess their sins to the "Reverend," and Lord Evelyn admits to a one-night stand with a young Chinese woman, Plum Blossom. Hope is not impressed with Billy's charade, and to please her, he confesses to everyone that he is not really Snake Eyes Johnson. Moon attempts to compensate by revealing that he is not a minister; he is Public Enemy Number Thirteen. The captain sends them both to the brig. Reno restores the mood of the Revival ("Blow, Gabriel Blow").

Moon tries to cheer Billy up ("Be Like the Bluebird"). Billy doubts he will ever see Hope again; he and Moon cannot leave their cell until they return to America. Their card-playing Chinese cellmates, imprisoned for conning all the third class passengers out of their money, will be put ashore in England. Moon and Billy challenge them to a game of strip poker, win their clothes, and disguise themselves again.

Billy, Moon, and Reno show up at the Oakleigh estate in Chinese garb. Billy and Moon tell Oakleigh's uncle that they are the parents of "Plum Blossom" and threaten to publicize Evelyn's indiscretion if he does not marry her. Oakleigh offers to buy them off and Moon gleefully accepts the cash, much to Billy and Reno's chagrin.

Billy and Reno find Hope and Evelyn, who are both unhappy with the prospect of their matrimony. Hope declares that she desperately wants to marry Billy ("The Gypsy in Me"). Billy spots Whitney and finally learns that Evelyn and Hope's planned marriage is really an awkward business merger. Billy realizes that Oakleigh is manipulating them all; Hope's company is really worth millions and Billy informs Whitney of that fact. Whitney offers to buy the firm from Hope at an exorbitant price, and she accepts. The marriage is called off since a merger is now impossible. Billy and Hope get married, as do Reno and Evelyn. A cable from the U.S. government fixes Billy's passport problems and declares Moon "harmless." Moon indignantly pockets Oakleigh's check and refuses to return it.