Teleportation

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

Physiological teleportation
The Kitlings and those affected by the Cheetah World could teleport away from their home to hunt for prey, and then return through what was a physical (or possibly psychological/instinctual) process. The ability could also be transferred as Ace, Midge, the Master and the Doctor all acquired the ability, although 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
A great variety of species and civilizations had access to teleportation technology. In general, a signal was needed for the teleport to work. The signal needs to be broadcasted 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 is low can result in an incomplete transfer causing part of units to not 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. (DWAM: The Germ War)

In the 51st century, Father Octavian and his clerics had teleportation devices that created an effect similar to that of a small tornado when the teleport was in use. DW: (The Time of Angels / Flesh and Stone) The Clockwork Droids of the same era also possessed 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 it’s range is at least enough to teleport from a ship in orbit to the Earth’s surface. It uses bracelets, which can detect whether any mishap has befallen the wearer, and can signal the system to hold the molecules of the wearer in stasis as a safety feature. The wearer can then be brought back to the ship, provided that their pattern has been stored in the buffers. (DW: Voyage of the Damned)
 * Sontarans had to use pods at areas 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, despite it being within a building. (TW: Children of Earth: Day Three)
 * The Raxacoricofallapatorians had teleportation technology. The Slitheen-Blathereen family linked their 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. (DWAM: 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)