Anti-gravity motorbike

The anti-gravity motorbike was driven in the 2074 Anti-Grav Olympics by the Doctor. After using it, he put it in his TARDIS's garage. Though he placed last on the bike, the Doctor found it useful for driving stunts that would normally be impossible.

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 for filming the The Bells of Saint John is the. Coincidentally, the original model of the Triumph Bonneville, the, was used by Jon Pertwee as the Third Doctor in The Dæmons.