Anti-gravity motorbike

The anti-gravity motorbike was a vehicle manufactured by the motorcycle company Triumph. It was driven in the 2074 Anti-Grav Olympics by the Doctor. After using it, he put it in his TARDIS's garage.

The Eleventh Doctor and John Jones rode the motorbike along the Berlin Wall in 1976 while tracking the Entity. After the two were blown into space, the Doctor used an inbuilt remote on its control panel to summon the TARDIS. (COMIC: Conversion)

The Eleventh Doctor again used the bike while foiling the Great Intelligence in 2013 London. Electing not to take the TARDIS into battle, he rode the bike to a cafe and later hacked into a Spoonhead, which used the motorbike to fly up the side of the Shard in London. (TV: The Bells of Saint John)

The Doctor eventually gave the bike to Clara Oswald, who used it in her commutes from Coal Hill School. (TV: The Day of the Doctor)

Behind the scenes
The motorbike used in the movies to represent the anti-gravity motorbike is the.