Hack Type: Advice
System: Spirit of the Century, The Dresden Files RPG, any Fate v3 variant

Just because it came to my mind and I wanted to archive it somewhere, this is as simple as the definition can get:

1. Something relevant to aspect X happens.
2. The player chooses to respond with Y.
3. Z happens as a result.*

* = Z is something complicated and/or horrible, and is not bound by the application of other game rules (like skill rolls, etc.)

Accepting or rejecting the compel is almost always (and by this, I mean if it's not, reexamine the compel) about accepting or rejecting Z, not X or Y. 

When in doubt, applying this as a litmus test is a pretty good way to go, I think.

EDIT: I've been asked to provide examples. Didn't any of you folks ever take algebra? :)

Aspect is Greedy.

1.) A crime boss offers you money to sell out your friends. 
2.) You sell out your friends for the money.
3.) As a result of this, your home base gets destroyed. (And probably, your friends are pissed at you, but they're PCs too, so that's for them to decide.)

or

1.) A crime boss offers you money to sell out your friends.
2.) You want the money, so you give him false information.
3.) As a result of this, he discovers the deception and puts a price on your head so large every bounty hunter within 1,000 miles wants to kill you.

New example. Aspect is Senior Assassin for the Black Mambo Society

1.) The Society asks you to do a job of questionable ethical value.
2.) You refuse.
3.) They kill your grandma.

or

1.) The Society asks you to do a job of questionable ethical value.
2.) You agree.
3.) Your grandma finds out and disowns you.

***

Why does it not become a compel until the third part? Two reasons.

The first is, because this could always happen instead:

1.) Crime boss offers you money to sell out your friends.
2.) You lie to get the cash.
3.) I ask you to roll Deceit against the crime boss' Empathy, to see if you successfully get the cash or not, and you invoke your Greedy aspect to help you on the roll.

See the difference? With a compel, you *automatically* decide the outcome is going to be dramatically or "plot" complicated, as opposed to using any other means of resolution. With compels, plot happens because of who you are and what you choose.

The second reason is, you cannot ever, ever, EVER take away a player's choice regarding his character's actions. Period. Even when we didn't know how to articulate these things as precisely as we do now, we knew enough to tell you on SotC page 44 that you can limit the available range of choices but not dictate precise actions. Aspects are not, and never should be used as, a railroading tool.

I'll be the first to admit the text in SotC could have been clearer on this point. It's clearer in Dresden.