Trade

This Siegebreaker boss just dropped a high-quality staff, but Barbarians obviously prefer other weapons. You could sell it, but perhaps there's a Wizard who just got a really nice Barbarian item...

Item trading was an integral component of Diablo II, allowing players to securely exchange multiple goods by placing them into an inventory-like screen before verifying the trade. For Diablo III, Blizzard wants to place a much higher emphasis on item trading. Since players can now see the damage-per-second (DPS) and sell value of each item, players can also make more informed decisions about trading.

It is currently unknown how (or if) trading will differ from Diablo II, or if Diablo III will incorporate feature such as auction houses to facilitate easier item trading.

Individual Drops

In Diablo III, any dropped items you see are yours to keep. This prevents others from hoarding valuable drops upon the death of a particularly powerful foe (especially Act Bosses). However, many high-quality dropped items will still be unusable by your character class; you may, for instance, have a powerful Wizard-only item drop when you are playing as a Barbarian. You could always sell it for a large amount of gold, which is a perfectly acceptable thing to do; however, perhaps you could get a nice item for your own class. Maybe someone just found something really nice for your character...