Dual wield
Dual wielding returns in Diablo III, in limited fashion.
The Barbarian is able to dual-wield virtually every one-handed weapon he can equip. (Though there are a lot of one-handed weapons he can't use; such as wands and short staves that the spell-casters use.) The Barbarian can not, however, dual wield two-handed swords, or use them with a shield as well, in Diablo III.
The Monk can also dual wield, but only with his class-specific fist weapons. It was initially said that he would have He will supposedly have a few skills that can only be used while wielding fist weapons.
The Wizard and Witch Doctor can not dual wield weapons, though the Wizard at least has the option of wielding a weapon in one hand and an orb (rather than a shield) in the other. Orbs offer offensive bonuses, almost like a second wand or other caster weapon, rather than the defensive bonuses or blocking that a shield provides.
The Demon Hunter can not dual wield melee weapons, but she can dual wield her class-restricted pistol crossbows. All other bows and crossbows are two-handed.
Dual Wielding Skills and Traits
There are no known skills that can only be used while dual wielding.
There is a trait, Frenzied Attacks that both the Barbarian and the Monk can enable. It provides them with (slightly different) critical hit bonuses while dual wielding.
Blizzard on Dual Wielding
Bashiok spoke about the theory behind dual-wielding, vs. using a sword/shield or a two-handed weapon, in early September, 2010. [1]