Goku is a monkey-tailed boy living all alone on Mount Paozu. One day, after he catches a large fish to eat, a girl in a car (being Bulma) almost hits him. He mistakes the car for a monster and throws it onto its side, but gets shot by Bulma in return. He thinks she is some kind of demon, but she ends up convincing him she's human, even though she does not have a tail. He invites her into his house since his dead grandpa always told him to be nice to girls. When they go in the house, Goku shows Bulma an orange glowing ball that he thinks is his grandpa. All of a sudden Bulma comes to life and asks if she can have the ball. When Goku protests, she brings out two more "grandpas", and explains to him the legend of the Dragon Balls and the Eternal Dragon. She offers to let him feel her up to get him to come along, but when that does not work, she tells him it will help him get stronger. He agrees, and they head off.
Later, in the forest, they are forced to stop because of a bull/ox in the road, who demands the girl. Goku ends up fighting the creature, which turns into a robot, and then a bat. Unfortunately, by then, his five minutes are up, and he turns back into Oolong, the pig. There is no time for apologies though, because Yamcha attacks. He demands all the capsules and money they have, but not before Puar recognizes Oolong and yells at him for his perverted antics at Shapeshifting School. Yamcha fights Goku, and appears to have the upper hand, until Bulma wakes up. This puts him into a state of shock and he is forced to retreat with the help of Puar.
Bulma, Oolong, and Goku are driving northward towards the next Dragon Ball, only to discover a huge metal tower in the distance. (Yamcha and Puar, who have been following them, stay in a cave nearby to keep warm.) Soldiers come out and "welcome" them to Muscle Tower, and Goku takes them all head on. He manages to enter the tower, only to face Sergeant Metallic. He finishes him off quickly though, and discovers (to his shock) that Metallic was a robot. General White of the Red Ribbon Army orders the remaining forces toward Goku, but he plows through them all, up into White's room. White then activates the tower's deadliest creation, Android 8. The android nearly strangles Goku, but refuses to kill him when ordered. As a result, White threatens to detonate the android, but Goku intervenes and saves him. The two make quick friends, with Android 8 explaining that he does not believe in fighting or killing. Goku complains that his name is weird, so he nicknames him "Eighter" for short. This ends in a snowball fight between the two while the tied-up forces (including White) look on.
Some time later, while driving in Oolong's house-wagon, they almost run over (and then almost fall off a cliff because of) Turtle. He explains that he is quite lost, and needs help getting back to the sea. After they bring him there, he says he has a reward which he will bring back with him the next day. So, Oolong, Goku, and Bulma spend the night on the beach. Goku wakes up early in the morning and tries to sleep in Bulma's lap, but freaks out when he removes her panties and discovers her lack of male genitalia. That morning, Turtle comes back bearing his "reward", the Turtle Hermit Master Roshi. Roshi first tries to summon the Immortal Phoenix for them, but when that fails (it apparently died from food poisoning, ironically), he calls forth the Nimbus Cloud. Goku is the only one of the bunch who can ride it, so it becomes his. Meanwhile, Yamcha and Puar watch the gang with interest.
While Goku's off on the Nimbus, Bulma discovers that the old man has a Dragon Ball. He offers to let go of it only if she shows him her underwear. She agrees, not knowing she does not have any on, and both Roshi and Oolong are pleasantly surprised. She is horrified after she goes in to change and finds her underwear still inside. There is no time for an explanation though, because General Blue of the Red Ribbon Army attacks with a fleet of battleships. When the situation seems just about hopeless, Roshi decides to use his legendary Kamehameha. He decimates the entire fleet with it, but Blue then orders his army of submarines to attack. Goku however, manages to learn the Kamehameha himself and destroys a good deal of the subs with it. But just as their situation is looking up, Goku is knocked out by a missile, and Bulma, Oolong, and Roshi are all captured by a battered Blue and his soldiers. Yamcha attempts a rescue, but gets caught along with Puar due to his phobia of girls. The five are carted off to prison near the Red Ribbon Army Headquarters. The next morning, Goku awakens to the beeping of the Dragon Radar. Finding himself alone, he sets out in search of the other six Dragon Balls (Blue, having missed the one on Goku's person, is executed for his failure). Goku fights through legions upon legions of Red Ribbon soldiers, while in the meantime, the others try to make their escape from the prison.
Eventually, they make it out, to discover Goku (carrying a pile of tanks) there to greet them. As Goku fights his way into Red Ribbon Headquarters, Commander Red and Staff Officer Black retreat with their six Dragon Balls to their last refuge. But when Black hears about Red's true wish to become taller, Black shoots him and swears to make the Black Ribbon Army ruler of the world. He brings out the Army's greatest weapon, a giant robotic suit called "Battle Jacket". The robot's Laser Blast destroys a huge swath of territory in its path, and nearly kills Goku, until he manages to knock it on its stomach and detonate the cannon. Black in his Battle Jacket is not out yet though, and Goku is eventually knocked out.
Luckily, Android 8 shows up. He puts everything he has into keeping the robot from killing the boy, but it is pretty clear that he is no match. Parts start to fly off of him, and he lands in a crumpled heap, next to Goku. Goku comes to, only to see the android die.
Saddened and enraged by Android 8's sacrifice, a new world of power suddenly awakens within Goku, as the ground shakes with his tortured screams. Black makes the mistake of egging him on, and Goku finishes him off with a gigantic Kamehameha. After the dust settles, the Eternal Dragon Shenron is summoned forth, but Bulma and Yamcha realize they do not need their wishes anymore. Goku then offers his own wish instead: to revive Android 8 and remove the bomb inside of him.