Lost Soul

The lost soul was first introduced in Doom's second episode, The Shores of Hell, but can be seen as early as E1M1 on the PlayStation and Saturn ports of the game where they can be spawned by a pain elemental hidden in a secret corridor.

Doom II made additional use of the lost soul by utilizing it as the projectile attack of the new pain elemental monster. The Doom manual gives this description of lost souls: "Dumb. Tough. Flies. On fire. 'Nuff said."

Doom RPG
In Doom RPG, the lost soul appears as a class of monster. There are three variations, identified by color: Lost souls can move three panels in a single turn instead of one, and will attack automatically once they are in an adjacent panel to the player, even if it has already moved. It attacks three times consecutively and can be damaged by the fire extinguisher.
 * Phantom (green)
 * Lost soul (normal colors)
 * Nightmare (blue)

Trivia

 * The lost soul is the only monster in Doom to not make any sound when alerted.
 * The lost soul is one of two monsters that do not leave a corpse (the other being the Pain Elemental).
 * Lost souls appear in the Diablo franchise, similarly appearing as floating skulls.