Diablo III – Do You Have to Stick Around to Get Co-op Loot?

No, the items that you get are entirely random (the item type is random, the number of affixes on an item is random to an extent, and the values of the affixes themselves are random within a given range for the item's level).

The only things that are set, as far as I know, are that higher-difficulty monsters (e.g. Champions/Rares/Bosses) have a greater chance to drop higher-quality items as well as in greater numbers, and that certain tiers of items can only appear on Nightmare, Hell, or Inferno difficulties.

There are reports of people receiving legendary drops from plain old white-named enemies, so anything is possible. (A little Magic Find doesn't hurt, either. :))

For the first kills on a major boss at Normal difficulty; you are guaranteed 2 rares as drops (regardless of MF etc.) Also a comment here suggests that one of them will be a class specific rare, which would explain the fist weapon drops for monks.