Fire

Fire was energy produced by rapid oxidation. The earliest splinter of Scaroth showed mankind how to make fire (TV: City of Death) and by roughly 100,000 BC, fire had become a precious commodity, as relatively few humans knew how to recreate it once it was snuffed out; in some tribes, this knowledge was held only by a select few.

The First Doctor and his companions Ian Chesterton, Barbara Wright and Susan Foreman encountered a tribe looking for this knowledge; Chesterton ultimately showed Za, a tribal leader whose predecessor was unable to give him the secret before dying, how to make fire. (TV: An Unearthly Child)

On one planet, the Fourth Doctor taught the Meerags how to make fire and use it against the giant mutants that were plaguing them. (COMIC: The Mutants)

According to Greek mythology, Prometheus stole fire from heaven and gave it to the first men. When the Fourth Doctor met Prometheus and recounted this story, the Olympian corrected him, saying that he actually stole the spark of life. (COMIC: The Life Bringer)

The Tenth Doctor once commented that fire was "so fun to look at! But bad for the skin!" (COMIC: Ground Control)

The Twelfth Doctor claimed to know of a race made of sentient gas who threw fireballs as a "friendly wave". (TV: Flatline)

Incidents involving fire
The First Doctor accidentally inspired Nero to start the Great Fire of Rome in 64. (TV: The Romans)

The Third Doctor saw an alternate Earth consumed by fire. (TV: Inferno) This memory was used against him by the Keller Machine. (TV: The Mind of Evil)

Ky used fire to ward off Solonian mutants. (TV: The Mutants)

During the Fourth Doctor's sacrifice by the Deons, fire was used to burn the ropes holding a rock above him. (TV: Meglos)

In Victorian era London, Leela savagely attacked the Linktons' teleportation device. It sparked and started a fire. This fire then went on to melt the Linktons present, as they were mostly made of wax. (PROSE: The Living Wax)

The Great Fire of London started when a Terileptil weapon overloaded in a building on Pudding Lane in London in 1666. Much of the city was burnt, but it proved helpful in clearing the bubonic plague from the city. (TV: The Visitation)

In 1994 Alaska, the Fifth Doctor set fire to Shaun Brett's memorial to his father to kill the Permians inside. (AUDIO: The Land of the Dead)

The Tenth Doctor used a burning stick to light a funeral pyre for. (TV: Last of the Time Lords)

In 2011, when a Teselecta disguised as the Eleventh Doctor was shot by River Song in order to fake the Doctor's death, it appeared to fall dead, and a funeral pyre was lit for it by Amy Pond, Rory Williams and a future version of River, using gasoline provided by Canton Everett Delaware III. The Doctor later claimed that his doppelganger was "barely singed" by the pyre. (TV: The Impossible Astronaut, The Wedding of River Song)

Jack Harkness once encountered a firebird, a creature literally made out of fire. (TV: Immortal Sins)

While possessed by the Beast, Toby Zed breathed fire. (TV: The Satan Pit)

In 1911, the destruction of Sutekh in the time tunnel set the priory on the future site of UNIT HQ on fire, burning it to the ground. (TV: Pyramids of Mars)

In a house in 1889, Sarah Jane Smith and Emily Morris discovered an echo from the future showing two children suffocating in a house fire. Using the chronosteel key, Emily saved the children. (TV: Lost in Time)

When the Ninth Doctor blew up Henrik's, the explosion set fire to the store. (TV: Rose)

Humans marked category 1 and category 0 were sent to overflow camps to be incinerated. (TV: The Categories of Life, End of the Road)

While attempting to maintain a hold on the fan controls for Platform One, Jabe burnt to death. (TV: The End of the World)

Pyroviles could breathe fire. One such Pyrovile disintegrated a human with its breath. (TV: The Fires of Pompeii)

In the early 21st century an emergency services officer tried burning the trees around Green Park tube station in London. The trees failed to catch fire as, according to the Twelfth Doctor, the trees "with[held] the oxygen" and "smother[ed] the fire". (TV: In the Forest of the Night)