Vesuvius

Mount Vesuvius, or simply Vesuvius, was a volcano located in Italy. On 24 August 79, Vesuvius erupted, destroying the Roman city of Pompeii. (TV: The Fires of Pompeii)

Two incarnations of the Doctor, the seventh (AUDIO: The Fires of Vulcan) and the tenth, (TV: The Fires of Pompeii) were present in Pompeii during the eruption, though they avoided meeting. Also present were two young brothers from the future named Peter and David. They had been chasing a Dalek through time, but had lost it in the lava thrown out by Vesuvius. The boys imagined it might be possible for people to one day find a Dalek at the bottom of the ruined Pompeii. (PROSE: Timechase)

In an alternative timeline, Vesuvius took much longer to erupt and the people of Pompeii evacuated in their boats. (PROSE: The Algebra of Ice)

The rocklike Pyroviles used a hollowed-out chamber in the mountain as part of their plan to terraform the Earth into a rocky wasteland to replace their lost homeworld, Pyrovillia. They used the energy from the volcano to power their operations, which cancelled the eruption. This presented the Doctor with a moral dilemma: by stopping the Pyroviles he would trigger the eruption. He would have to allow Pompeii to be destroyed to save the world. With the support of his companion, Donna Noble, he triggered the eruption. The explosion was as powerful as twenty-four nuclear bombs. The force of the blast cracked open a rift in time which lasted for a second. Its effects rippled backward in time, allowing the people of Pompeii to see the future. The eruption also destroyed the Pyroviles. Although almost all of the residents of Pompeii perished, one family was saved by the Doctor. This was a fixed point in time, though the Doctor was unaware he had caused it at first. (TV: The Fires of Pompeii)

Captain Jack Harkness claimed to have used the eruption as part of one of his cons against the Time Agency on multiple occasions, though he would never stay for "Volcano Day". (TV: The Doctor Dances)

The Seventh Doctor's companion Melanie Bush made a replica of Mount Vesuvius out of papier mâchè while in primary school. (AUDIO: The Fires of Vulcan)

Behind the scenes
The Fires of Pompeii's corresponding Confidential episode, The Italian Job, showed a camera crew actually visiting Vesuvius for some shots. David Tennant himself chose to come as well to tour the mountain and the excavated ruins of Pompeii and remarked that Vesuvius still being active to this day lent a bit of intrigue and excitement to things. Both David and the camera crew could still see smoke and steam issuing from vents.