Currently - while in a party each player will see their own drops from each kill.
This could mean that after killing a zombie I see a sword drop, and you may see a shoulder slot item drop. Or I see nothing drop, while you got an axe.
Obviously while in a group you're killing faster, and this could translate to an exponentially increasing number of drops with each additional player in your party. However, it's balanced in such a way that the drop % is pulled back a bit with each additional player (I'm simplifying it, but that's what it boils down to). This keeps it from being almost detrimental to not play with a full party, while still giving a nice increase to the amount of drops if you do.
From this system it seems quite a few people got the impression that you'll never see items drop that you can't use. For instance, a Barbarian will never see a dagger that only a Witch Doctor can use. This isn't true. There is no effect, or at least no currently intended effect, to restrict which items which classes can or can't see for their respective drops. It's still intended that you could see an item that your class can't use. It's easy enough to drop the item, ask if anyone can use it, or just sell it off of course.