Wights

A wight is a reanimated corpse, raised from the dead by the White Walkers to act as their servants.

Season 1
During a battle with the White Walkers, Will of the Night's Watch sees the corpse of a young wildling girl standing and walking. The corpse now has blue eyes similar to those of a White Walker. Will flees before she shows any other capability.

The corpses of two members of Benjen Stark's scouting party, Othor and Jafer Flowers, are found in the outskirts of the Haunted Forest near the Wall. They are taken back through the Wall to Castle Black, and Sam notes that despite being dead for weeks, rot hasn't set in. Later that night, they reanimate as wights, and Othor attacks Jon Snow and Lord Commander Jeor Mormont. The creature survives every kind of attack, including impalement and having its arm cut off, until Jon Snow throws a lamp at it, setting it on fire. Both corpses are then burned completely, with Samwell Tarly pointing out their likely nature to all present.

Characteristics
A Wight is a recently deceased body reanimated by magic. Many stories say White Walkers alone have the ability to do this. Samwell Tarly noted that the Wights he had encountered had been dead for weeks, yet there was no sign of rot or decay. Regardless of eye color while alive, a Wight has icy blue eyes, like its masters the White Walkers. Animals are extremely agitated by Wights. They lack the ability to speak, communicating only in bestial growls and hisses. A Wight is almost indestructible and can withstand an injury that would normally be fatal, including stab wounds and removal of limbs. Even amputated limbs will still move around on their own, and will only stop moving after complete dismemberment (when every joint has been disconnected, which is very inefficient).

However, Wights are very susceptible to fire. Their flesh is extremely flammable; it will easily catch fire and continue to burn if exposed to even a small amount of flame.

In the books
In the Song of Ice and Fire novels, the Others (the book term for the White Walkers) are able to animate corpses to serve them as footmen. The Others are also shown to be capable of reviving any dead animal as a Wight, such as horses, dogs, bears, and even aquatic animals.

A Wight's physical condition will roughly match the condition the corpse was in when it was reanimated. A corpse that was killed in a relatively non-violent way and which is resurrected soon after death will still seem relatively lifelike. In contrast, a corpse that died violently or which was resurrected long after it died and it had already begun to decompose will still look like a maimed, rotting corpse. Reanimation will halt the physical process of rot and decay, but otherwise it does not restore previous damage. A corpse with a broken leg won't magically have the leg healed when it is reanimated into a wight.