Items in Diablo III vary in rarity, just as they did in previous game versions. Your Magic Find adventuring stat will have an effect on your drops.
And then you have the Rare (yellow) items, which can have as little as one affix (strange, but true), and as many as 6 affixes (though some affixes are multiple lined due to multiple effects)
Of course, the Set (green) items are still there, and as in D2, they still give partial set bonuses for multiple parts, but there's no all-encompassing bonus for actually completing an entire set anymore.
Lastly, the Unique (orange) items... Ostensibly the most powerful items in the game. In Reaper of Souls, these and the set items will be the legendary drops that will totally change your character and the way you play the game, when you find them!