Quivers are a special off-hand item type only usable by Demon Hunters in Diablo III.
"Not merely a container for arrows and bolts, the quiver often contains mystic properties. Some quivers provide easier access to projectiles and thus quicker rates of fire; others confer on their arrows the crackle of lightning or the sharpness and impact of thrown spears."— Game Guide(src)
Similarly to Arrows and Bolts from Diablo II, the Quivers may be equipped in the off-hand slot alongside a ranged weapon (Bow, Crossbow, or Hand Crossbow). As of patch 2.4, Quivers can even be equipped with a one-handed melee weapon; a Quiver cannot be used, however, with dual Hand Crossbows.
In Diablo III, arrows are infinite, so Quivers do not limit the number of shots. They are also not shown on a character model, but all pants on Demon Hunters do show quivers in some way, sometimes even two at a time.
All Quivers have a guaranteed Attack Speed increase (usually 15–20% regardless of level) instead of flat damage the other off-hand items provide. This affix is free, and does not count towards the total 6-affix limit, but cannot be rerolled at the Mystic. (When increased attack speed was nerfed on virtually all items in patch 1.0.3, Quivers were the only item exempted.)
They can roll core and all-armor stats, one Socket (Quivers are treated as Armor for gem bonuses), Area Damage, Critical Hit Chance, bonus damage against Elites, reduced skill cooldowns, increased damage of any skill, reduced resource costs, increased maximum Discipline, Hatred regeneration, Life %, Life per second, Thorns, extra healing, and various 'chance on hit' effects.
There are no set Quivers.