There were numerous species of pterosaurs, ranging in size from small (TV: Invasion of the Dinosaurs) to ones with forty-foot wingspans. (PROSE: Blood Heat) No one knew how they took off from the ground to fly. (PROSE: EarthWorld)
In an alternate universe, an especially large type of Pterosaur were used by the Silurians as steeds. With a forty-foot wingspan, they could easily carry a Silurian. They were used as war steeds in times of battle and would cling to the side of the airships. (PROSE: Blood Heat)
In an alternative timeline in which all of history happened at once, Pteranodons were considered to be vermin. They were found in places such as Hyde Park and would chase people. (TV: The Wedding of River Song)
Pterodactyls were among the species placed aboard the Silurian Ark to repopulate the Earth with once the catastrophe the Silurians incorrectly predicted had passed. Flocks of Pteranodons were known to live in the Ark's beach-like environments.
The Rani genetically modified Pterodactyls to attack Koturians and bring her black blood and tissue samples from them. Sometimes they would also bring back the whole individual for her experiments. The Sixth Doctor recognised them as the work of the Rani thanks to the gold sheen on their wings. (PROSE: Something Borrowed)
Vortisaurs were creatures living in the Time Vortex which were similar to pterodactyls. The Eighth Doctor and Charley travelled with one called Ramsay for a while. (AUDIO: Storm Warning) They were forced to release Ramsay back into the wild after several failed domestication attempts. (AUDIO: Minuet in Hell)
Behind the scenes
A Pteranodon appears in the Doctor Who -themed Google doodle game. If the player goes to the egg which is hidden in a bush (returning it to its nest), the Pteranodon will later help the Doctor cross the lava river to get back to his TARDIS.
Doctor Who: Battles in Time
According to DWBIT 7, Pterosaurs were also native to the planet Raxas, and along with the other Raxas dinosaurs, proved to be more than a match for a Dalek attack. They picked up Daleks, grabbing them between their feet, flying high into the air and dropping them to their deaths on the rocks below.
According to DWBIT 27, the Perrincott were a pterosaur-like species native to the planet Senkus Sha.