If you're a veteran player, the real tip is at the end. It works on PC, not sure about console.

Killing an act boss (Andariel^&, Duriel, Mephisto, Baal) when your quest is active drops better loot than if the quest isn't active. What is better loot? 0% chance to drop only scrolls/keys/potions, higher chance to drop higher quality gear (magic, rare, set, unique). It's not drastic, but it's worthwhile if you're doing lots of runs, see here for relative drop rates.

If the character that delivers the final blow to the boss hasn't yet completed that boss's quest in that difficulty, the boss will drop "quest loot".

Under normal conditions, that would complete the quest for that character, however...

Killing an act boss with a character whose quest for that boss displays "Quest cannot be completed" will trigger quest loot, and also won't complete the quest for that character (i.e. you can repeat this step ad infinitum).

The "cannot be completed" state is caused by one of 2 things:

• (Less likely) Your character joined a game where the boss could have been killed for the quest, but someone else completed the quest, so you can no longer complete it. The boss is dead in this game.

• (More likely) Your character joined a game that was created by a character who already killed the boss for a quest in this difficulty. The boss is alive in this game, but you can't complete the quest by killing him. If you kill the boss while "cannot be completed" is displayed on the boss quest, he will drop quest loot. Note that someone else might've already killed the boss in this game if you joined a public game.

What's the "real tip"?

If you're looking to take advantage of this "glitch" on one account, you have a character (A) that's already completed a given boss quest in one difficulty, and another character (B) that hasn't (e.g. Hell Mephisto).

Enter the lobby on character A, and create a password protected game, and exit as soon as you load in. Return to character select, switch to character B, re-enter the lobby, and join that same game. Some guides will tell you to wait 5 minutes to "perm" the game but I've found it's not necessary if you do it fast enough. This trick actually worked on Blizzard servers in normal D2XP, and seems to be even more forgiving now.

^& Andariel can be bugged in any given difficulty, look up guides for that

E To add: I've seen several comments here from people who had this backwards: if your character has already completed a boss quest, you won't get "quest loot" from killing the boss, whether or not the quest is available to other players when you kill him. The determination is made by the player who gets the final hit on the boss. I believe this is common knowledge, but please correct me if you believe I'm wrong here.