The main focus of Diablo 3 is combat. Every character is built for dealing large amounts of damage. There are currently eight types of damage that all have different attributes.
Physical Damage - Critical hit: Deals double damage.
Arcane Damage - Purple - Critical hit: Arcane crits "silence" targets. (Silenced targets can not cast some spells, such as a Skeletal Summoner or Goatman Shaman resurrecting fallen minions.)
Cold Damage - Blue - Critical hit: Cold crits freeze targets for 2 seconds.
Fire Damage - Red - Critical hit: Fire crits set targets ablaze, adding DoT to the initial fire damage.
Lightning Damage - White - Critical hit: Lightning crits stun targets for 2 seconds.
Disease Damage - Green - Critical hit: Disease crits deal an unknown bonus. Resisted by Poison resistance. Diseased units suffer a damage debuff; they take more damage and deal less.
Poison Damage - Green - Critical hit: Poison crits deal an unknown bonus. Resisted by Poison resistance. Poisoned units suffer a health debuff; their regeneration and healing is lessened or reversed.
Holy Damage - White - Found mostly in Monk skills.
Spell Damage works much like physical damage does; spells now come with a fairly low base damage, like weapons, and that value is augmented by attributes, spells, traits, and equipment bonuses, all of which factor in to the final spell damage. Equipment with +%spell damage is quite common, and mage characters will want to collect as much of that type of equipment as possible. This means that magic find gear will now destract from your overall power, making it much harder to stack magic find like casters did in Diablo 2.