Teleportation

Teleportation was a form of matter transmission and could be either a process of physical/psychological will or a technological one.

Physiological teleportation
The Kitlings and those affected by the Cheetah World could teleport from their home to hunt, and then return through what was a physical (or possibly psychological or instinctual) process. The ability could also be transferred as Ace, Midge, the Master and the Doctor all acquired the ability. It was not permanent in the majority of those who were affected. (DW: Survival)

The Eight Legs of Metebelis III could also teleport, both themselves and the Humans that they hung onto, most likely through the psychic link that was developed between the Eight Legs and the Human. (DW: Planet of the Spiders)

Unicorns were capable of teleportation. (EDA: Unnatural History)

Technological teleportation
Many species and civilizations had teleportation technology. In general, a signal was needed for the teleport to work. The signal needed to be broadcast close to the person or item being teleported. The signal could also be reworked to teleport a person back after they had teleported away. (DW: The End of the World, Boom Town) Teleportation, when power was low, could result in an incomplete transfer, causing part of units to fail to materialise. (NSA: The Pirate Loop) Teleportation tended to leave behind an energy residue and a distinctive tang in the air. (TWN: Something in the Water)

Human teleportation
Humans developed teleportation technology around the 20th century with the TOMTIT device. (DW: The Time Monster)

In the early 21st century, the Project Indigo was created. It was reverse-engineered from Sontaran technology. (DW: Journey's End)

In the mid-21st century, the T-Mat system was developed. (DW: The Seeds of Death) In the aftermath of the invasion and the Thousand Day War, the T-Mat network was replaced by the Interstitial Mass Transit System. (NA: Transit)

The Disinfectodroids created by Acme Industries teleported trash to another planet. (DWA: The Germ War)

In the 51st century, Father Octavian and his clerics had teleportation devices that created an effect similar to that of a whirlwind when the teleport was in use. (DW: The Time of Angels / Flesh and Stone) The Clockwork Droids of the same era also used a short-range teleporter (DW: The Girl in the Fireplace) The Time Agency vortex manipulator also had teleportation capabilities. (DW: The Sound of Drums)

Before the year 5 billion, long-range teleportation was forbidden under Peace treaty 5.4/cup/16. Despite this, Lady Cassandra O'Brien possessed one. (DW: The End of the World)

Other species

 * The planet Sto (or at least Max Capricorn Cruiseliners) had a form of teleportation, the full range of which is unknown. However its range was at least enough to teleport from a ship in orbit to the Earth’s surface. It used bracelets, which could detect whether any mishap had befallen the wearer, and could signal the system to hold the molecules of the wearer in stasis as a safety feature. The wearer could then be brought back to the ship, provided that their pattern had been stored in the buffers. (DW: Voyage of the Damned)
 * Sontarans had to use pods for dematerialisation and rematerialisation. (DW: The Sontaran Stratagem/The Poison Sky)
 * The Marinusians used travel dials to travel around Marinus. (DW: The Keys of Marinus)
 * The 456 appeared on Earth in "pillar of fire", allowing them to teleport into a specially made tank within a building. (TW: Children of Earth: Day Three)
 * The Raxacoricofallapatorians had teleportation technology. The Slitheen-Blathereen family linked theirs to their spaceship and their bracelets. (SJA: The Gift)
 * The Vinvocci also had teleporters hooked up to their wristwatches. (DW: The End of Time)
 * Rammzi used a teleport to travel the universe, searching for the best restaurants. (DWA: Fried Death)
 * The Sycorax had teleport technology. (DW: The Christmas Invasion)
 * The Linktons could teleport across truly vast, inter-galactic distances. Their technology required gold for power. They once attempted to invade Victorian era London with it, but were repelled by the Fourth Doctor and Leela. (PHS: The Living Wax)
 * The Cybermen had a teleportation device connected to their ship inside a shop in Colchester. (DW: Closing Time)