Motorbikes were a form of ground transport, typically able to carry one or two riders. They were common on Earth in the 20th and 21st centuries.
The Monk's TARDIS briefly took the form of a motorbike when the First Doctor reprogrammed its chameleon circuit, ultimately changing its outer form to that of a police box. (DW: The Daleks' Master Plan)
A number of UNIT troops used motorbikes. (DW: The Ambassadors of Death)
Billy had a motorbike called The Vincent, which had a passenger sidecar. The Seventh Doctor drove it for some time during his encounter with the Bannermen. (DW: Delta and the Bannermen)
In Perivale, the Seventh Doctor faced Midge in a duel which involved the use of motorbikes. (DW: Survival)
In 1999, the Eighth Doctor and Grace Holloway stole a motorbike from a policeman in San Francisco while trying to get to the Institute for Technological Advancement and Research. That same day, another policeman rode his motorbike (with faulty brakes) through the open doors of the TARDIS, immediately turned around, and sped off in the opposite direction. (DW: Doctor Who)
Blaid Drwg (Bad Wolf) was a motorbike gang. (TM: Jetsam)
Sarah Jane Smith used her Sonic lipstick on a motorbike. It sparked and disorientated the rider. (SJA: The Lost Boy)
Rory Williams and Amy Pond pursued their daughter Melody on a motorbike in 1939 Berlin. To do the same, the Teselecta was able to change its shape into a human riding a motorbike. (DW: Let's Kill Hitler)