Jasper and Stewart

Jasper and Stewart were a pair of twin bats who took up long-term residence within the TARDIS during the Seventh and Eighth Doctor's lives. They lived in the TARDIS for "a long time," and the Doctor regarded them as old friends. Jasper was the more adventurous and approachable of the two, while Stewart was notably stoic and dutiful.

Though the bats had the run of the ship, they appeared to have established a permanent residence in a seldom-used annex of the TARDIS's enormous library wing, near the "H"s.

Biography
Jasper and Stewart reacted in alarm when the Master and Chang Lee entered the TARDIS's Cloister Room, dropping from the overheard framework and quickly escaping. (DW: Doctor Who)

Curious about a new presence in the TARDIS's library annex, Jasper landed on the back of a bookcase and crept along the shelf, trying to catch a glimpse of Carolyn McConnell between the books. When Carolyn pulled out the hematology book directly in front of Jasper and saw him she screamed (an understandable response, she was researching Vampires) which caused Jasper to panic and take off.

There was much screaming and flapping before the Doctor arrived and plucked Jasper from the air to give him chin-scratchies and pettings with baby-talking to calm him down. He then formally introduced Jasper to Carolyn and released him back to the rafters.

Stewart watched the whole affair from a nearby girder with a barely-concealed sense of dry amusement. (EDA: Vampire Science)

Later, when Sam Jones brought the Doctor back to the TARDIS after being imprisoned and starved by the Tractites, he collapsed and slept for 28 hours. The bats helped watched over him, perching on his recovery bed or cuddling in Sam's lap, and when Sam herself had to sleep Jasper accompanied her while Stewart remained to stand guard over the Doctor.

Much later when an empty TARDIS summoned Sam Jones back to it, Jasper and Stewart flew into the console room to greet her and perched on her shoulders for snuggle-times. (EDA: Seeing I)