The protoss have spent thousands of years studying the nature of time and space and as a result, their ability to manipulate it far exceeds that of other races. Arbiters can weaken space-time, tearing rifts in the fabric of space-time, creating a vortex linking another location to the arbiter's location; warp prisms are able to perform a similar ability through the psionic matrix, as can motherships. Carriers are equipped with teleportation platforms that can quickly deploy protoss warriors to a planet's surface.
In addition, teleportation mechanisms are built into power suits and light armor suits. When a protoss wearing one of these suits nears death, they disappear in a flash of bright light, and are teleported to safety. Primitive and superstitious civilizations have attributed this to supernatural causes. These mechanisms can also be activated manually.
Stalkers are also able to blink— a form of short-ranged teleportation that allows a user to appear or disappear in a flashing pillar of light. Some dark templar also have an ability similar to the stalkers' blink, which is referred to as shadow dash, in which the user could teleport a short distance by appearing and disappearing in a cloud of smoke and shadows. Adepts are able to teleport using a form of psionic transfer. An offensive form of teleportation was Lightning dash, in which the user teleported a short distance before reappearing in a flurry of energy. This energy damages and stuns all enemies that surround the user. 
Terran teleportation fields were invented by Transmatter Inc. Although not as advanced as protoss teleportation technology, terran teleportation devices are able to quickly move living organisms and objects short distances within structures and science vessels via teleportation pads.
Teleporting a solid object into another solid object can result in a "telefrag".
Transmatter made several attempts to improve on the technology, but they were all failures. Another terran attempt at a teleportation system was the MH-232 Teleportation system, but there was a terrible accident and it malfunctioned. There was a valiant attempt to manually control the teleportation matrix without the automated computer system, but it eventually failed.
In contrast, the Kimeran Pirates had an advanced teleportation system aboard their ship, the Kimera, which didn't require a fixed piece of technology to transport people on and off the ship. However, the technology required accurate positioning information which came from transponders. If those were knocked off-line, the teleportation system could not be used. By the End War, terran engineers had devised a FTL-based teleportation system for the Minotaur-class battlecruiser and the Hercules-class dropship, allowing for tactical combat jumps across short distances.
In the original StarCraft, zealots, bengalaas, and kakarus all used the same blue flash animation upon death. In the case of zealots, this has since been explained as being from their teleportation mechanism.