The Capsule Corporation spaceship (カプセル宇宙船) is a ship made by Capsule Corporation that was used to travel throughout space.
Capsule ship 1
The first Capsule Corporation spaceship was made for Goku by Dr. Brief out of the scraps of Goku's original spaceship that brought him to Earth. Brief made the spaceship with a bedroom, a bathroom, and a training room that included an intense gravity simulation machine that goes up to 100x Earth's gravity. Goku used the spaceship to travel to Planet Namek while training using the Gravity Machine over the next five days, slowly increasing the gravity from 10x to 20x to 50x to 100x. After four days of training, Goku relaxed and rested himself on the fifth day, arriving just time to save Gohan, Krillin, and Vegeta from the Ginyu Force. After transforming into a Super Saiyan for the first time, Goku told Gohan to take Piccolo and Bulma to the spaceship that he used to get here (although Gohan, Piccolo, Bulma are later teleported from Namek to Earth thanks to Porunga). After Goku's long fight with Frieza, Goku didn't have enough time to make to his spaceship so he had to use the Ginyu Force's Attack Ball. The first Capsule Corporation spaceship was destroyed during Planet Namek's destruction.
Capsule ship 2
The second Capsule Corporation spaceship was made completely from scratch by Dr. Brief due to Chi-Chi's constant demands. After its completion, Chi-Chi, along with Master Roshi, Yajirobe, Puar and Oolong board the spaceship to go to Namek. However, it shut down completely upon lift off and nearly exploded. It is unknown if the second Capsule Corporation spaceship had the gravity simulation machine that was in the previous model.
Capsule ship 3
After returning to Earth with it, Vegeta also used its Gravity Machine (which was modified to 500x gravity) to train for the Androids in three years time in the opening of the Trunks Saga. Vegeta accidentally destroyed it when overstraining himself in his training and was hospitalized as a result.
After a later one was built, Vegeta used it continue his training and Piccolo used it to go to New Planet Vegeta after sensing Broly's ki level in his Legendary Super Saiyan form, and allowed Krillin, Oolong, Roshi, and the Shamoians to use it to escape from New Planet Vegeta before it was destroyed by Comet Camori.
This model was also implied to contain a transwarp device as shortly after New Planet Vegeta was destroyed it warped in, although it ended up receiving dents in the process. It was also seen in Dragon Ball Z: The Return of Cooler and Plan to Eradicate the Saiyans.
Video game appearances
Goku uses the Gravity Machine inside the ship to train before arriving on Namek in Dragon Ball Z II: Gekishin Freeza, Dragon Ball Z: Legend of the Super Saiyan, and Dragon Ball Z: Goku Gekitōden. Goku also uses it to go to Planet Kanassa during his journey to Namek in Gekishin Freeza.
The ship also appears in Dragon Ball Z III: Ressen Jinzōningen and Dragon Ball Z: The Legacy of Goku II for Vegeta's training, in Dragon Ball Z Gaiden: Saiyajin Zetsumetsu Keikaku and Shin Saiyajin Zetsumetsu Keikaku - Uchū-Hen for the Z Fighters' journey to the Dark Planet, and in Dragon Ball Z: Harukanaru Densetsu. In The Legacy of Goku II, a side-quest has the Z Fighters using the Capsule Ship 3 to accompany all of the missing Namekians to New Namek and bring the ship back to Earth. Once on New Namek, the Z Fighters confront Cooler in his final form. In Dragon Ball Z: Shin Budokai - Another Road, the Z Fighters travel to New Namek in a Capsule Corporation spaceship in order to prevent Future Babidi from using the Namekian Dragon Balls, as well as to bring Future Dende to Earth; the ship they use is from Future Trunks' timeline and it goes faster than those of their time according to Krillin.