A rocket was a device that moved by exerting a large amount of force in the direction opposite to travel. Many spacecraft were rockets.
Transport use
The use of rockets on Earth had been temporarily abandoned during the 21st century in favour of the T-Mat. The Second Doctor, Jamie McCrimmon and Zoe Heriot travelled in a rocket from Earth to the Moon. Professor Eldred, a scientist who had a long history with rocketry, had constructed the rocket as part of a plan to take Man beyond the moon. The engines were burnt out when the rocket arrived on the moon. (TV: The Seeds of Death)
Warlike use
On Skaro, the Thals used a rocket to hit the Kaleds citadel with a distronic bomb. They had a slave force consisting of mutos and captured Kaled soldiers pack the nosecone with the toxic explosives. Sarah Jane Smith was one of the workers. (TV: Genesis of the Daleks)
In 2065, Space City stocked up on rockets as part of the battle preparations for the Space War against the Astrans. (COMIC: Ceasefire — But War Tension Mounts...)
In the nuclear war between Atrios and Zeos, the Marshal of the former attempted to hit the latter with nuclear rockets. (TV: The Armageddon Factor)
Recreational use
According to the Fourth Doctor, a Mars-Venus rocket run was held in a unspecified time. (TV: Robot)
Other uses
The Rani tried to employ a space rocket to make clash a load of Loyhargil and a strange matter asteroid. (TV: Time and the Rani)