Cars, or automobiles, were a common means of transport for humans on Earth in the 20th and 21st centuries. By the end of the first decade of the 21st century, there were eight hundred million cars. (TV: The Sontaran Stratagem)
History
20th century
In London in 1924, while on their way to the British Empire Exhibition, the Ninth Doctor explained to Rose that black was the old silver for that time. (PROSE: The Clockwise Man)
In 1926, Agatha Christie's car was left abandoned by a lake on the night her memory lapsed in the struggle against the Vespiform. (TV: The Unicorn and the Wasp)
In 1951, Eddie and Barbara Smith died in a car crash. (TV: The Temptation of Sarah Jane Smith)
In 1963, Ian Chesterton drove himself and Barbara Wright in his car to 76 Totter's Lane to solve the mystery of Susan Foreman. (TV: "An Unearthly Child")
Forester drove a big American car, which caused P.C. Bert Rowse to swerve his bicycle straight into a muddy ditch. (PROSE: Planet of Giants)
UNIT had two black Jaguars that followed the Second Doctor and Jamie McCrimmon after they emerged from International Electromatics following their meeting with Tobias Vaughn. (TV: The Invasion)
A black Jaguar with dark-tinted windows was used by a C19 operative at one point to spy on James Stevens during his investigations into UNIT. (PROSE: Who Killed Kennedy)
During his exile on Earth, the Third Doctor drove a yellow roadster called "Bessie". (TV: Doctor Who and the Silurians) The Brigadier procured Bessie to persuade the Doctor to work with UNIT after the Doctor had expressed fondness for a similar vehicle he had "borrowed" shortly after arriving on Earth. (TV: Spearhead from Space) A time eddy snatched the Third Doctor, along with Bessie, out of 20th century Earth into the Death Zone on Gallifrey. (TV: The Five Doctors) Bessie remained on Earth in UNIT's care when the Doctor regained his time travel knowledge. It was used by his fourth, seventh and eighth incarnations on subsequent visits to Earth. (TV: Robot, Battlefield, PROSE: The Dying Days)
Brigadier Lethbridge-Stewart occasionally travelled in a chauffeur-driven Ford Zodiac staff car. (TV: Spearhead from Space to TV: The Dæmons intermittently) He drove the car himself on one occasion, when he used it as a getaway vehicle to escape from the Space Centre following its takeover by General Carrington. (TV: The Ambassadors of Death) His own personal cars were a blue Austin Maxi (TV: Terror of the Autons), a blue 1929 Humber 16/50 open tourer, Imperial model, (TV: Mawdryn Undead) and a white Mercedes convertible. (TV: The Green Death)
Two white Citroën 2CVs were used as transport by Colonel Trenchard and his prison officers on Fortress Island, the location of the high-security prison where the Master was confined. (TV: The Sea Devils)
After the Master abandoned the hovercraft he had used to escape from the Third Doctor and the Royal Navy (TV: The Sea Devils), he hitched a lift in a Ford Cortina belonging to Jack Harris, a travelling salesman. The Master killed Harris, who had proved immune to his hypnotic powers, with his Tissue Compression Eliminator and, after hanging Harris's shrunken corpse on the driving mirror, used the car to travel to Devil's End. (PROSE: The Eight Doctors)
While still affiliated with UNIT "post-exile", the Third Doctor also briefly used a different car with a "space-age" look and hovering/flying capabilities. (TV: Invasion of the Dinosaurs, Planet of the Spiders)
Sarah Jane Smith drove many small cars over time, while a companion of the Doctor (TV: Robot, School Reunion) and afterwards. (TV: A Girl's Best Friend, Invasion of the Bane)
In 1987, Peter Tyler was killed in a hit-and-run incident. Rose Tyler saved his life, causing a massive paradox that made Reapers appear. The car that had killed him disappeared and reappeared across the same stretch of road. To heal the rip in time, Pete ran in front of the looping car, killing himself and returning the timeline to normal. (TV: Father's Day)
Shou Yuing drove a light blue Citroën 2CV, which was commandeered by Brigadier Lethbridge-Stewart to get to Vortigern's Lake, and later borrowed by Brigadier Winifred Bambera and Ancelyn to return to the Gore Crow Hotel — during which Bambera used the car to run through a road-block made up of Morgaine's knights. It was prior to this particular incident that Ancelyn confirmed to Bambera that cars did not exist at all on Arthur's World. (TV: Battlefield)
21st century
During his eighth incarnation, the Doctor used a Volkswagen Beetle that he could drive into his TARDIS. He garaged it in its own alcove. The Doctor traded it for information from the Faction Paradox concerning Samantha Jones whilst in San Francisco in 2002. (PROSE: Vampire Science, Unnatural History)
Mickey Smith used a car belonging to Sarah Jane Smith to break into Deffry Vale High School by driving straight through the building's glass doors. (TV: School Reunion) Mickey Smith also drove a tow truck that Jackie Tyler borrowed from Rodrigo in order to open the Heart of the TARDIS. (TV: The Parting of the Ways)
John Ellis used a car to commit suicide by carbon monoxide poisoning. (TV: Out of Time)
Donna Noble owned a dark blue Peugeot 307, though she and her mother took turns driving it. She had a pivotal moment while driving her car, where turning left brought about her first meeting with the Tenth Doctor. When elements of the Trickster's Brigade caused her to instead turn right, an alternate world was created in which she never met the Doctor, causing his death and dramatic changes to the history of Earth. She travelled in time to correct the error, once again turning left and restoring events to their original course. (TV: Turn Left) The car was among 400 million cars fitted with the ATMOS devices which eliminated carbon dioxide emissions; when the Sontarans activated the devices, Wilfred Mott was nearly choked to death by gas that was inside the car but Sylvia saved him by breaking the windscreen with an axe. (TV: The Sontaran Stratagem/The Poison Sky) After having her memory wiped by the Doctor, she went Christmas shopping with her fiancé Shaun Temple and angrily warned a nearby traffic warden "Don't you touch this car!". Somewhat intimidated, the traffic warden quickly left. (TV: The End of Time)
Brian Hopley, Maggie Hopley's husband, died in a car crash. (TV: A Day in the Death)
Luke Rattigan created ATMOS, a device which stopped cars from producing CO2. In actuality, ATMOS would also release a gas that would suffocate humans, but allow Sontarans to grow clones. ATMOS was also used to control cars and drown those that opposed Rattigan. The Tenth Doctor narrowly escaped from one of these attempts on his life, but journalist Jo Nakashima was not so lucky. (TV: The Sontaran Stratagem/The Poison Sky)
When the population of Earth was warp shunted away by the Automatons, the planet's cars were left in place, rather than being allowed to crash. (TV: The Empty Planet)
In 2008, when Prisoner Zero escaped, Rory Williams and Amy Pond used Rory's red Mini to get to the Royal Leadworth Hospital, in order to meet the Eleventh Doctor there. (TV: The Eleventh Hour)
Also in 2008, a Blowfish driving a red Chrysler Crossfire sports car led the Torchwood team in a high speed chase in Cardiff.
In 2011, Jack Harkness, Gwen Cooper, Esther Drummond and Rex Matheson, who would eventually form a revived Torchwood team, escaped the CIA in Esther's Mini Cooper. (TV: Rendition) Gwen was later forced to kidnap Jack by car, to take him to Olivia Colasanto's people. (TV: Immortal Sins)
In 2011, the Eleventh Doctor drove a '59 Edsel wagon whilst in Utah. (TV: The Impossible Astronaut) Amy Pond and Rory Williams later wrote a message in a field using their Mini to attract the Eleventh Doctor's attention. Shortly after the TARDIS materialised in the field, Mels drove into the field with a Chevrolet Corvette, being chased by the police. (TV: Let's Kill Hitler)
Far future
In the far future, cars such as the New Earth car could hover. (TV: New Earth) During the time that New New York was under quarantine, the survivors trapped below lived for many years travelling in such cars. (TV: Gridlock)
On Xirrinda, human tourists used auto-piloted cars. Gellen Jenkins used one to escape from the Rain of Terror. (PROSE: Rain of Terror)
On Red Rocket Rising, cars were solar powered. (AUDIO: Blood of the Daleks)
Alternative timelines
River Song's world
In the alternate timeline created by River Song's refusal to kill the Eleventh Doctor, some cars were transported by large balloons. London had a large number of these cars. (TV: The Wedding of River Song)
Parallel world
In a parallel world, the poverty of Great Britain following the destruction of London by the starship Titanic meant that the country had far fewer ATMOS installed cars. (TV: Turn Left)