Diablo – Legendary sets for increased magic find

As of the 1.03 patch, Magic Find only affects the drops when a monster dies. It has no effect on chests, barrels, or other containers.

I don't yet have enough MF gear to test it properly, but information is nevertheless from personal experience, from the existence of the Treasure shrine, and from Blizzard comments such as the one quoted in this Q&A session, in which they acknowledge that switching weapons right before a boss dies will make its dropped loot better, which is why there's no fast weapon-switch concept like there was in Diablo II.

Below level 60, there's none, apart from farming areas with many monsters in them.

However, at level 60, the most effective way should be to do "extended boss rushes":

First you have to know that Blizzard has actually implemented mechanics to balance drops so that purely farming bosses isn't more effective in farming for rares than it is to farm areas with normal monsters/champions, namely the Nephalem Valor Buff .

The original quote from Bashiok is this (although the thread containing it has since been deleted):

You will not be farming bosses. Bosses won't drop the best loot, they won't even drop really great loot. Part of Inferno and our intent with getting people out into the world and hunting and killing lots of different things is putting the best loot on rare and champion packs, and the great thing about rare and champion packs is they have random affixes. They're like a box of chocolates. Murderous, snarling, blood-soaked chocolates. You're not going up against a boss where you know "Build A" is the best way to minmax against it because it has abilities and resistances X, Y, and Z. What is the best build vs. an "Arcane Enchanted, Teleporter, Frozen, Knockback" skeleton pack? Got that figured out? Cause it's not going to be the best against the next pack you come across, and you're going to want to kill that one just as much.

However, there's something extra to this: There's no official word form Blizzard about this (yet), but as many players (among them, me) are currently experiencing, it strongly looks like major bosses (such as the Skeleton King and The Butcher in Act 1) have at least two guaranteed rare-drops as long as you have five active stacks of Nephalem Valor. "Strongly" means that I have done about 10 runs on the Butcher so far and he has dropped two or more rares (along with a higher-than-usual amount of magic items) every single time.

This means that probably the most effective way is to get five stacks of Nephalem Valor as fast as possible, and then farm a certain boss in the Act that you're playing.