An offshoot of the FUDGE system, FATE is an open source RPG mechanic/generic system. Characters are described with Aspects, Skills, and Stunts.
Aspects are short descriptions of your character that give you a mechanical bonus when appropriate and can be anything from descriptions like "Raised by Gypsies" to "Knight" to phrases like "You should all listen to me" or "But it works in theory!". The player can make Aspects up, to flesh out his character as he likes, without being limited to lists and the like. Players must spend a "fate point" from a pool in order to use these aspects to their advantage. The GM (or opposing players) may invoke these aspects to the characters disadvantage by paying one of their fate points to the player. Aspects can be used from the location ("Foggy," "Cluttered Furniture," "On Fire!"), equipment may have Aspects on them, and you can perform Maneuvers that don't damage your opponent but place temporary Aspects on them or the setting that can be used once for free.
Skills are used in the traditional way, to provide a straight bonus to die rolls when trying to pass tests. The core rules suggest various ways to implement them, from lists to freeform application. Skills are limited to a pyramid; to have a skill at +2, you must have more than one skill at +1. A skill at +3 requires at least two +2 skills, and those require at least three +1 skills under that. Players who don't take at least +1 in a skill can still use that skill at +0 or at -1, depending on the setting.
Stunts are narrow and use more powerful applications of skills, similar to "Feats" in Dungeons and Dragons. They may allow a +2 advantage to a skill in a narrow application ("Grease Monkey: +2 to Repair if you are working on a vehicle"), substitute a skill in place of another ("Money Talks: spend some cash and use Resources in place of Contacting"), allow unusual equipment, always-on access to resources (ie. photographic memory, cybernetic implants) or a specific exceptional maneuver ("Thump of Restoration: hit a device to make it work immediately for X turns, after which repairs rolls are at -1")
Damage during conflict is accumulated as Stress, and each character has multiple stress tracks for physical and social/mental stress. Some FATE implementations add a third stress track for sanity or wealth. Taking X hits in conflict means marking off the Xth box on the stress track AND all below it. If the Xth box is already marked, cross off the next highest empty box. If this goes over the top, the player must assume a Consequence --a new negative Aspect that reflects an appropriate injury to the conflict (ie "battered and bruised", "laughingstock," "shellshocked"). These start out minor, but must be of increasing severity as these injuries pile up, to a maximum of three. These aspects can be invoked for free by opponents Stress boxes are wiped clean when conflict is finished, but the Consequences stick around until the character can recover. Rather than suffer Consequences, a loser may offer a a fate point and a Concession, a way of bowing out gracefully. The opponent can take the fate point and the loser's narration of the loss, or refuse with a fate point of their own to push the fight to the death as it were.
The players use Fudge dice, four six-sided dice marked with two + signs, two - signs and two blank sides (basically a d3). When rolling, this produces results between 4 pluses and 4 minuses (ie. from -4 to +4), with a bell curve centered on a 0 (zero) result. The roll is then added to the Skill being used (along with any bonuses Stunts and Aspects invoked with fate points). Because of the average zero result, you know you will perform at your skill's rank most of the time, with decreasing deviations up or down. Modified rolls that meet the difficulty are successes, with excess that can be spent for improving the quality of your success (ie. getting it done faster, improving the quality of the crafted item, inflict more damage, +bonus to your counterattack).
Feng Shui, a very early precursor to the system, used an alternative rolling scheme that produces similar results on a much wilder, less-stable curve: rolling two d6 dice of different colors and subtracting one from the other. The Dresden Files RPG even offers it as an alternative rolling scheme, though it cautions that it means much more-variable results than FUDGE dice.
To add some color to the +1 and -1 math, FATE rates each of the results and skill levels on The Ladder.
The first canonical version is called "pre-3rd", and was published as Spirit of the Century. Evil Hat said that they would finish 3rd edition for their next big FATE game Dresden Files RPG, then publish a setting-less "core" book and a Creative-Commons standard reference document online.