GM fiat  gets a bad rap. It often carries connotations of “Because I said so,” which, while within your rights as the GM, is also generally a bad idea.
But in and of itself, there’s nothing at all wrong with GM fiat. It’s my favorite way to handle awarding experience . It can be helpful in starting up a campaign — hell, it’s the cornerstone of the moldy-yet-still-useful “You all met in a tavern, but you trust each other with your lives” approach to party creation. Although that approach certainly has its problems, it remains popular despite the fiat.
But what about choosing the result of a critical NPC die roll — or even skipping the roll and just saying “X happens”? Having a monster abruptly break off combat with a near-dead PC, even if doesn’t make any sense? Saying “Alice, your character decides to get up and leave the bar”?
In those three situations, I’d say #1 is just fine, #2 is cheesy but usually considered acceptable and #3 is completely unacceptable. What do you think? And what role, if any, does GM fiat play in your campaigns?