Yes, FATE 'complications' (is it complications or consequences? ) are one of the more intriguing ways of modeling cinematic injury/jeopardy that I've seen in an RPG, and I'd love to hear more detail from someone who has a better grasp of and more experience with them.
Sorry it took me so long to get back to this [MENTION=996]Tony Vargas[/MENTION]. Let me take a stab at it.
I'll start by discussing only physical damage. To avoid talking about the full mechanics of FATE, let's assume for the moment that all the dice have been rolled, and it has been determined that the character is going to take some damage - usually called points or "shifts" of stress.
1) Stress Boxes
In FATE games, a character has some number of "stress boxes", usually between 3 and 5. The fist stress box is worth one. The second is worth two. The third box is worth three, and so on. When a character is taking damage, the player can check off a box, just one, to absorb the damage. If he's taking only one point, he can check off the first box. Is she's taking two points, she has to check off the second box. If you are taking damage, and the box you want to check off is filled, you must roll up the stress track. If you already took two points from an earlier attack, so your second box is checked, you must check the third box, even though it could hold more, you check off the whole box. Tough luck, that.
If you are in a situation where the damage you take must roll off the top of your stress track, you are "Taken Out" of the fight. You can no longer act, and your opponent gets to narrate what happened to you - maybe you are dead, maybe you are unconscious, or what have you. The rules suggest that PC death is often a pretty boring result that leaves players feeling bad, and suggest the GM save it for really dramatic moments, but it isn't off the table here.
Checked stress boxes do not impose any penalties on the character. Stress boxes clear *quickly*. After the conflict, if you get a minute to breathe, *all* your stress boxes clear. They are just stress, not wounds.
2) Consequences
Now, in addition to checking off boxes, a player may choose to take consequences to absorb stress. Exactly how many consequences you can take can vary (some games have bennies that allow you to take more consequences, some variants have different consequence structures). But, a typical structure is that a character can take one Mild, one Moderate, and one Severe consequence.
A Mild Consequence will absorb two stress. A Moderate consequence will absorb four stress. A Severe consequence will absorb six stress.
While a player can check off only a single stress box from a given hit, he may take multiple consequences in addition to that stress box. So, if you take a really massive hit, you can soak it up with a stress box and multiple consequences.
Consequences also carry some penalty for the character. They are "Aspects" that can be used by opponents to get a bonus on die rolls against the character. The opponent who caused the character to take the Consequence gets one use for free. Later uses will cost a Fate point.
Consequences also don't go away as quickly. In order to clear a Consequence, a character must first complete some action relevant to fixing the problem. If, for example, they have the consequence, "Sprained ankle", they should get some first aid. The action to clear the Consequence must be taken in some period of relative calm, not in the middle of a fight. After succeeding at that action, they must also wait some time. How long depends on the level of the Consequence. For a Mild consequence they must wait through a scene before the Consequence clears. For a Moderate Consequence takes an entire session to clear - if you took the clearing action in the middle of this session, the thing will clear in the middle of the next session. A Severe Consequence takes an entire scenario (an adventure, basically) to clear up. So long as the consequence is there, opponents can tag it and use it against you.
Some FATE games also have a stress track for Mental and/or Social stress - this puts these things on the same mechanical basis as physical combat. But you still only get the one set of Consequences.
FATE also adds the idea that, rather than get Taken Out, a character can choose to Concede. You can, at any time, interrupt any action before the roll for it is made to Concede. You get a Fate Point for doing so, and you get to control the manner you get taken out (with a bit of agreement from the GM). So, if you Concede, you can stipulate that you are out of the fight, but *not* dead or completely at your opponent's mercy.