FUDGE is a Universal System for (relatively) freeform tabletop roleplaying games — designed to support the sort of game where players don't want to spend any more time than absolutely necessary dealing with rules and tables. The "core rules" are freely available online.
FUDGE uses custom "three-sided" dice — really six-sided dice labeled [+][+][ ][ ][-][-] note . The core mechanic has you rate each of your character's skills on a seven-point scale, from Terrible to Superb, based on how good a result you'd expect from your character when they use that skill — "Great Swordsman" is not just a description of a character, it's the skill that you'd put on their character sheet. When it comes time to use the skill, you roll four FUDGE dice, and move along the seven-point scale, one point upward for each [+] and one point downward for each [-]. The rules do assign numerical values to each result, and provide for numerical comparisons between results, but GMs are encouraged to just look at the name of the result and come up with some game effects to fit.
Another system that uses FUDGE-based mechanics is FATE, the core rules for Spirit of the Century, The Dresden Files RPG, Ehdrigohr, Mindjammer, Atomic Robo, and The Small Folk, along with a few more indie properties, including Divine Blood. Grey Ghost Press, the publisher of the original FUDGE books, sells Sourcebooks for it: Deryni Realms and Terra Incognita. FUDGE is the core system for Seraphim Guard's HeartQuest line of shoujo-style roleplaying games.
If you came here looking for the book series of the same name, see Fudge.