Train

A train was a grouping of vehicles that moved, particularly over metal rails, transporting passengers or freight.

On Earth
The Fifth Doctor claimed that he had always wanted to drive a steam train as a boy after landing his TARDIS at Cranleigh Halt. (DW: Black Orchid)

The Doctor kept a model train set in his TARDIS, which he constructed over a period of several years until it eventually became a microcosm of its own. (ST: Model Train Set, EDA: Vampire Science, Genocide)

In 1863, the Third Doctor and Charlie Fisher used a train engine to escape from the Confederate lines after their hot air balloon was shot down. (TVA: Backtime)

In 1879, Queen Victoria had planned to take the train to Aberdeen, but was forced to go by coach when a fallen tree blocked the line, as arranged by the Brethren. (DW: Tooth and Claw)

In 1898, Ian Stratford got the train from Paddington station to the town of Three Sisters. (EDA: The Banquo Legacy)

In 1909, Jack Harkness and a group of soldiers under his command were travelling through Lahore by train when the soldiers were killed by Fairies. (TW: Small Worlds)

In 1979, the Fourth Doctor and Romana took a train while in Paris. (DW: City of Death)

Circa 1990, the Seventh Doctor and Sarah Jane Smith took a train to Royal Albert Hall which was abducted by the Kalik. (DWM: Train-Flight)

In 1993, a Fortean Flicker transported a group of train passengers to Hogsumm. (NA: The Highest Science) They were later returned to their own time by Romana II. (NA: Happy Endings)

In 2050, due to the Oroborus consuming time, all the trains in London ran on time, even if they were several hours late, and some trains even arrived before they had left. (K9TV: Oroborus)

Alternate timelines
In a universe where it was always 22 April 2011 at 5:02pm, Amy Pond took the Eleventh Doctor aboard a train headed for Area 52 in Egypt. (DW: The Wedding of River Song)

On other planets
On an unnamed planet, the Daleks used a train for transport. The Second Doctor crashed the train by removing a section of the track, causing it to derail. (TVC: The Exterminator)

One human colony world which was mostly ice used skitrains, which had runners instead of wheels. (MA: Cold Fusion)

On the stormy planet Tempest, the only way to safety traverse the wastelands was by monorail trains. (BNA: Tempest)

In a heavily polluted city on an unnamed world, the Fourth Doctor assisted the Guardian Angels in finding the correct train track which would lead them out of the city and to the countryside. However, when he arrived there in the TARDIS and waited for them, they never arrived, and he concluded that they didn't make it, which was perhaps just as well since the countryside was just as polluted as the city itself. (DWM: End of the Line)

In the Matrix on Gallifrey, the Fourth Doctor found himself trapped on a recreation of a train line, his foot caught in the tracks after the points changed, while Goth drove a train toward him. The Doctor managed to free himself and jumped clear at the last second, and the train then vanished. (DW: The Deadly Assassin)