More fantasy games than you'd think are "somebody's D&D houserules" or an attempt to do D&D "better". Even games that aren't medieval fantasy can trace their lineage back to some primordial D&D or a first order heartbreaker.
A good example of this is Call of Cthulu, which uses the Rolemaster system, which was one of the first D&D fantasy heartbreakers.
As far as I know, there's Fate offshoots, Apocalypse World offshoots, ultralights like Lasers and Feelings, and whatever the fuck Chuubo's is.
Fate was explained in thread. There's an SRD with all of the core rules, the Accelerated offshoot, and IP scrubbed alternate rules for several of the games made via a rolling Kickstarter.
Be advised that it is a build your own system more than an out the box game. If you want to jump in and game, I would suggest the Atomic Robo RPG or if you can cop it, Dresden Files Accelerated. Also, the Fate Point Economy is nonfunctional unless players compel themselves constantly, in which case it is merely spotlight hogging.
Apocalypse World is the next step closer to improv storygame from Fate. Everything works off of a 2d6+mod roll, with specifically coded rolling situations (called moves) saying what happens on a three tiered level of success. The GM is called to make things up on the fly as much as possible, using the results of the moves and a series of narrative prompts on their side: Fronts (setpieces), Threats (antagonists), and GM Moves (responses to player rolls).
It's easier for experienced TTRPG players to grok than Fate, but if the GM is off, the game falls to pieces. If your players don't like an RNG weighted to have bad things happen to them, the game will fall apart. Also, watch out for Sex Moves in certain games (Monsterhearts, AW 1st and 2nd).
AW games are self contained and really easy to procedurally generate, so there are a lot of hacks.
Ultralights explain themselves. Chuubo's is Amber Diceless fucking Noblis