Crystal

Crystals had a great variety of valuable (and in some cases, strange) uses.

Radiation and/or luminiscence
The planet of Metebelis III was known for blue crystals which emanated radiation. The crystals mutated spiders from Earth into the intelligent and telepathic Eight Legs. (TV: Planet of the Spiders)

Radioactive Hymetusite crystals powered both Skonnan and Nimon technology. The Skonnan Empire demanded tribute of these crystals from the people of Aneth. (TV: The Horns of Nimon)

More trivially, Terileptils used vintaric crystals for lighting. (TV: The Visitation)

Time travel and time manipulation
Xion crystals were one component of the Doctor's TARDIS. When they got misaligned, this caused it to go off course. (COMIC: Pinball Wizard) In place of a time rotor, the Thirteenth Doctor's control console had a large crystal that glowed orange while in flight. (TV: The Ghost Monument)

The Crystal of Kronos enabled to create TOMTIT and to summon the eponymous Kronos. (TV: The Time Monster)

The Borad used kontron crystals to create the Timelash. (TV: Timelash)

The War Lord SIDRATs, sub-par imitations of Time Lord TARDISes, lacked a green crystal from Gallifrey that was necessary for their time control units. (PROSE: Doctor Who and the War Games) Another Gallifreyan crystal, the blue Kyfred Gem was considered by the Twelfth Doctor to be the rarest crystal in the universe. (GAME: Lost in Time)

Communication
The Black Guardian gave crystals to Vislor Turlough and Menlove Stokes to direct them in his plans against the Doctor. (TV: Mawdryn Undead, PROSE: The Well-Mannered War)

Psychic energy
Certain crystals could focus and/or harness psychic energy. The people of Manussa used the Great Mind's Eye, a crystal artificially created in zero gravity, to accidentally create the demonic Mara. The Little Mind's Eye destroyed the Mara. (TV: Snakedance)

The Great One, leader of the Eight Legs, for this reason sought the Great Crystal which the Third Doctor stole from her planet. (TV: Planet of the Spiders)

Sentient crystals
The Xylok resembled crystals. They valued purpose more than anything else. Stored in computer form, they were capable of communicating with human computer software, storing vast amounts of information, accessing databases, hacking teleports, containing beings, defending itself and many, many more functions. One such Xylok was known as Mr Smith and worked with Sarah Jane Smith to defend Earth. (TV: Invasion of the Bane et al.)

The Spherions were a species of crystals, reproducing by incubating their young in organic matter. Unaware that it was possible for organics to be sentient, the Spherions used the Calaxi as incubators following their homeworld being colonised. When they crossed paths with the Eighth Doctor and Josie Day, the two relayed to them that organics were living beings, with the Doctor finding them a new planet. (COMIC: Music of the Spherions)

Unspecified powers
The Eternity Crystal was a crystal of immense power created by the Darksmith Collective for the Krashoks which was capable of reanimating life. (PROSE: The Dust of Ages-The End of Time)

Other uses for crystal
The Crystal Bucephalus, a restaurant, was named after its sculpture of the legendary horse of the same name. (PROSE: The Crystal Bucephalus)

Frank claimed several times that his friend Jane was into crystals. (PROSE: The Party in Room Four)

The Doctor's sonic screwdriver used a crystal, similar in composition to the ones from Metebelis III. The Tenth Doctor ejected it from his screwdriver to draw a handful of Eight Legs away from himself and Martha Jones. (COMIC: The Forgotten)

Behind the scenes
According to the audio play adaptation Seven Keys to Doomsday, the Crystal of All Power, capable of good or great evil, destroyed the Masters of the planet Karn. Consequently, the Masters broke the crystal into seven small crystals scattered across the planet, which the Daleks sought to implement their Doomsday Plan. The Doctor also sought the pieces. This wiki considers neither Seven Keys nor the original play, Doctor Who and the Daleks in Seven Keys to Doomsday, a valid source.