The Sixth Doctor and Melanie Bush once hired a green convertible Volkswagen Beetle from Bertie's Rent-A-Bug in Australia. Some time later Mel was surprised to find that, instead of returning the car as he'd promised, the Doctor had kept it aboard his TARDIS. Furthermore, he had replaced the car's collapsible roof with one the same colours as his trousers and added a green sunstrip across the windscreen which read "The Doc" on the driver's side and "Companion of the Moment" on the passenger's side. Mel chided the Doctor for his dishonesty and talked him into at least repaying Bertie's for the cost of the car (although it is unclear if he ever did, as they were subsequently distracted by a reunion with Evelyn Smythe and a confrontation with John Doe and the Cylox. (PROSE: Instruments of Darkness)
The Eighth Doctor kept a purple Volkswagen Beetle in an alcove in his TARDIS, which he and Sam Jones drove on numerous occasions. (PROSE: Vampire Science, Longest Day, Seeing I) By one account, after the car was destroyed, the Doctor traded its remains to a Faction Paradox cultist in 2002 for information. Faction Paradox planned to take the car back in time and melt it down, ensuring its own steel would be used to build it and creating a "nice little paradox." (PROSE: Unnatural History) The Doctor replaced the Bug with a Mini Metro which had a Volkswagen "VW" badge glued to its bonnet; one of his companions put a note on the car which read, "It's just not the same, Doctor. Get rid of it." (PROSE: Interference - Book Two)
Later in his timeline, the Eighth Doctor again owned a purple Volkswagen Beetle, registration number WHO 8, which he kept parked in 1970s London. (AUDIO: Eyes of the Master) He found it again when stranded in 2020 London, but decided to loan it to Jim rather than make use of it himself, citing the high maintenance costs. (AUDIO: Lost Property)
Sarah Jane Smith had a red Volkswagen Beetle she called "Ethel", which was blown up. (AUDIO: Comeback) In 2010 Sarah Jane had an old yellow Beetle, registration number JTB 329K, which she gave her son Luke upon his departure for the University of Oxford. (TV: The Nightmare Man)
Behind the scenes
One famous Non-Doctor Who use of a Volkswagen Beetle was in the Disney franchise The Love Bug. In 1973, Jon Pertwee appeared on Disney Time, where he acted partially in-character as the Third Doctor and interacted with Herbie, comparing the VW to his car, Bessie. He then introduced The Gnome-Mobile before sitting on Herbie's trunk as the car backed out of shot.