After wrecking Popeye's ship and stealing away Olive Oyl, hero of Arabic legend Sindbad decides to test him and his ever-resilient new rival's strength in order to prove their supremacy as the "most remarkable, extraordinary fella" of Sindbad's menagerie island.
Popeye the Sailor, accompanied by Olive Oyl and Wimpy, is dispatched to stop the dreaded bandit Abu Hassan and his force of forty thieves.
Popeye sails to Goon Island in search of his Pappy. He finds the place populated by the imposing, but ugly, goons, and a "no humans" sign. His imprisoned pappy at first ignores him, but when Popeye is caught by the goons and carried off, his can of spinach lands near Pappy and it works just as well on him as it does on Popeye.
Popeye and Olive Oyl visit a rodeo.
Popeye, Olive Oyl and more King Features Syndicate comic strip characters are invited on a cruise hosted by Professor Grimsby, a mad scientist who wants to eliminate laughter from the world. When the ship is held hostage on his island lair, it's up to the much more action-inclined Mandrake the Magician, Steve Canyon, and Flash Gordon (among others) to save the funnymakers from their eternal inprisonment.
Popeye and Olive, adrift on a raft, land on what apparently is Africa, and are immediately battling elephants and gorillas (also a moose!). Popeye eventually battles an entire menagerie at once - after first gulping down a can of spinach, of course.
Popeye skates over to Olive's house to give her a Christmas present: ice skates of her own. While he's teaching her, Bluto skates up and gets fresh; of course, Popeye fights him. When Olive rejects Bluto again, he sends her careening on an ice floe towards a waterfall.
Olive tells Popeye and Bluto that she loves a man in a uniform, so they try to sign up at the recruiting station - that can only take one of them.
Popeye takes Olive mountain climbing. Bluto sets various traps for them along the way.
Popeye is wooing Olive on the phone when Bluto comes over. He overhears, taps into the line, and impersonates Popeye. They proceed to have a high-wire fight on the telephone lines outside Olive's house.
Olive is moving out of her apartment; she's hired Bluto to move her things, but Popeye comes over to visit and won't be shown up.
Olive preaches the need for brotherly love on the radio. Popeye, hearing this, does a number of good deeds: helping two workmen raise a safe, straightening a wrecked car, and helping two boys sneak into a baseball game. But when he tries to break up a fight, it's more than he can handle alone. Olive and her followers come along and try to help, but it's too much for them, too. Of course, once Popeye has his spinach...
Popeye applies for a lifeguard job when he sees Olive in the pool, but Bluto also wants the job (and Olive). The manager, Wimpy, asks them to demonstrate their skills in a contest. Popeye does well, until Bluto demonstrates lifesaving and first aid on him.
Popeye and Olive are taking a ferry run by Bluto. When they find out the fare, they decide, with Wimpy, to build a bridge. Bluto does what he can to sabotage this plan - until spinach time, of course.
Popeye takes Swee'pea to the zoo and spends most of his time rescuing the tot from the various animals.
Wimpy is working for Bluto in his diner and trying to filch all the food he can eat. Popeye comes in and orders roast duck, but Wimpy grabs the drumsticks, then coats it with pepper sauce. Popeye walks out in anger and Bluto comes after him. Wimpy takes advantage of the resulting battle to load up on hamburgers.
Popeye teaches Olive the art of self-defense, which comes in handy when a woman boxer flirts with him.
Popeye is running a women's gymnasium next door to Bluto's cabaret. Seeing Popeye's greater success with women, Bluto dresses in drag and challenges Popeye to various feats of strength.
Popeye drives up to take Olive for a ride, but Bluto in his much fancier car does what he can to spoil their jaunt.
Popeye's ensemble is rehearsing the opening of the Poet and Peasant Overture (with interpolations of the Popeye theme and "I've Been Working on the Railroad"). Maestro Bluto drops in from next door to conduct and play violin and show Popeye up. Popeye plays horribly until he unlocks the previously unexplored artistic benefits of spinach.