Three classes can dual wield various types of weapons. The Barbarian is able to dual-wield every one-handed weapon he can equip. The Monk can also dual wield all one-handed melee weapons. The Demon Hunter can not dual wield melee weapons, but she can dual wield her class-restricted Hand Crossbows. (All other bows and crossbows are two-handed.) The Wizard and Witch Doctor can not dual wield weapons, though they can equip class-specific off-hand items (Sources and Mojos) that add damage and offensive bonuses.
While dual wielding, the character alternates weapons each attack. Dual wielding grants a +15 Attack Speed % bonus.