I'll repeat some of the choices already made - Fate Core, Fate Accelerated and Cortex Prime. I'd also add Fantasy Age 1e as a different, simpler TTRPG to play the genre with, ableit IMO it needs some rules tweaking. I also like Mythras Classic Fantasy, but I need to know the party of players is up for the crunchy combat it offers. I'm also a fan of what I call D&D derivatives, i.e. True20 and 13th Age. While those cling closer to the bone (D&D 3.5 for True20 and 4e for 13th Age) than the others I listed, they're still vary enough from their origins to provide a different play experience.
I've also used Savage Worlds for the Classic Fantasy, but I'm not particularly keen on any of the 1st or 3rd party settings - Hellfrost is the only one that's piqued my interest enough to run some adventures. When using SWADE for the genre, I want to homebrew to the extent of creating my own worlds, which is what I did with my myrkRinna and Mythical Oyashima settings. I guess it comes down to all SWADE's tools and modularity giving me a desire to homebrew in entirety, rather than adapt or use prexisting. I know I'm mostly alone in that, because I've participated in many a forum thread over the years, with highly enthused GM's achieving good results with their adapatitions of the World of Greyhawk or Eberron, to name just a few.