UPDATED:
Legendaries can drop at any time, anywhere, albeit rarely. With the Loot 2.0 updates, new heroes from lvl 1-59 will get a guaranteed legendary drop for the first kill of The Butcher, Belial, Azmodan and Diablo.
Characters below level 11 are unlikely to find Legendary items, because they have a minimum level requirement. Currently there are no Legendary items available below level 11. (source)
For level 60 characters, you should get a guaranteed legendary drop from Diablo every time you kill him after resetting all of your quests and working your way back to him.
Higher tiers of Torment supposedly include an increase in legendary drop rates, but the exact amount of the bonus has not been disclosed. It doesn't seem to be major, though, so you should pick a lower tier of Torment over a higher one if you will kill significantly faster in the lower tier.
Note, however, that some legendaries will only drop in Torment I - VI.
Original answer:
Yes, there are set and legendary items.
Many of them will be available through crafting, requiring the recipe to drop.
Others will drop randomly, but extremely rarely. This can happen at any level, as not all legendaries are high level gear.
The best legendaries will be Inferno drops.
However, it has been stated that the very best items in the game will not be the set items or legendaries. Instead, the very best will be Inferno level randomly-generated rares.
Blizzard want you to farm elite packs rather than bosses and have adjusted the guaranteed drops from bosses and elite packs in the 1.0.3 patch:
The Nephalem Difference
It’s no secret that our goal for the end-game item hunt is players hunting monsters packs, building to five stacks of Nephalem Valor, and then killing a boss. While we’re seeing a lot of that occurring, what we’re missing is people feeling like it’s worthwhile to continue onward after killing a boss.
To help hit that goal we’re lowering the number of guaranteed Rare items on bosses when you have your full five stacks of Nephalem Valor from two guaranteed Rares to one guaranteed Rare (you still have a very good chance at multiple rares, it's just no longer guaranteed). In exchange, all champion and rare packs will now drop a bonus guaranteed Rare item when you have your full five stacks of Nephalem Valor. The change benefits players with more overall drops, and a reason to push to continue progressing.
Best Answer
Most people that I'v eseen run it does it in story mode as the waypoint is right next to him. As for drop rate, he's considered a 'boss drop' which gives more loot than elites, thus more chances at legendary items.
Most people who does this run wears a Mara's Kalideoscope which completely nullfies his poison damage. I suppose the advantage is greater for HC players since there is zero chance of dying, even on T6 when wearing that amulet.
Whether its worth it or not is pretty subjective I'll leave that up to you to decide.