Unique Monsters is a generic name for one of the types of Elites, a counterpart of Champion Monsters. While Champions are a group of equally powerful monsters, Uniques are single empowered creatures, sometimes accompanies by lesser (and weaker) followers, which form a retinue of sorts.
Diablo IIEditIn Diablo II, Unique Monsters are stronger and have semi-random magical bonuses, nearly always followed by minions. Most of the Unique monsters you find will be randomly spawned throughout the game. However, Super Unique monsters will always spawn in every game and in the same location. Their name is always highlighted in golden color.
The 'Unique' category is reserved for special monsters that usually spawn for quests, events or just rarely in the same location, being similar to Diablo II Super-Uniques. Their names are colored in purple, and instead of listing affixes beneath the name, almost all of them have a title.
Super-Unique monsters are not officially making a return in Diablo III. However, some Unique monsters spawn in every game, including all bosses: aside from the encounters vital to the game's storyline, some of them are certainly present every time players log in. These Uniques can be considered Super Uniques for that reason.
Like Champions and Rares, non-boss Uniques have affix skills (and sometimes even their own special abilities), but they always have a fixed set of 1 to 4 affixes regardless of the player's level, even if those affixes are not allowed for that level. Some monsters may even have affix combinations normally not allowed, such as Plagued + Desecrator. Their affixes deal more damage than those of Rare and Champion monsters on same difficulty, and they generally have considerably more Life.
In very rare cases, Unique monsters may have extra skills, such as triple attack speed or additional elemental damage, that are not available through affixes. Some of them can have random affixes as well.
While Unique Monsters have access to Missile Dampening affix, they will never spawn with Avenger, Health Link, Horde and Fire Chains. They will also normally not have Minions, although some Unique monsters spawn in densely infested areas and will not fight alone. There are Unique monsters who can summon other creatures at will.