Curse is a dispel type that is inflicted by various bosses, mobs, and most commonly, by warlocks (Curse of Weakness for example. See Warlock abilities for a full list). Curses do only exist as debuffs, not as buffs. In most cases, they only have a negative effect without doing damage, but some of them are actually DoTs (such as Curse of Agony). The border around a Curse type effect's icon in a player or mob's debuff bar is purple.
List of curse removing abilities
Curses are dispellable with the following abilities: