I pretty much hang around the Heroic Fantasy genre, and my thoughts on running it are very different from my thought's on playing it or otherwise. But Pathfinder 2e is definitely my go-to for running. Shit just works. I cannot express how much I appreciate the encounter budget actually being accurate instead of just a vague shoulder shrug like earlier systems.

As far as other genres go... I've run Scum and Villainy for sci-fantasy crime dramas, and it wins by doing absolutely nothing! I'm just not enough of a Sci-fi Greg to run more in the genre, heh.

• Fantasy - D&D 5.0 for the most part, but we are having a good time with DragonBane
• Space Opera - FFG Star Wars. Yeah, the dice are a bit rough to get used to after D20 systems and people find it rather "swingy," but I think it is pretty good
• Heroes / Avatar (TLAB) - Prowlers and Paragons (Ultimate Edition)
• Horror - I think the last time we played a horror game it was Dark Conspiracy
• Cyberpunk - Shadowrun. I haven't played 6e or Anarchy, but I have played 1e - 5e. Looking forward to trying Cy-Borg at some point.

• Fantasy: Mostly anything other than D&D if I'm the one running it. I'll play D&D all day long, but I prefer not to have to run it. Magical Kitties Save the Day is fantastic, very well thought out and incredibly easy to teach, learn and run. Though it is best for it's specific setting, I have attempted a modified version of the system with "converted" D&D characters and it was an absolute blast.
• Fantasy (take 2): Mazes is another one I really like mechanically, though I have yet to run it. Based on reading it and watching actual plays: the mechanics in it are, simply put, elegant. And it allows for super easy/basically instantaneous conversion of old D&D modules/dungeons/monsters if you want to use those.
• Supers: Wild Talents - This game has the most unique dice rolling system I've ever used and I love it. Once you grok it, it's pretty fantastic. Similarly it has an insanely flexible system to build any kind of powers you want, but in a structured, semi-balanced way. It definitely takes some getting used to for how completely different everything is from any other system I've ever looked at, but it's very well put together and flows really well after a little practice.
• Horror: Dread is so good for horror games. The automatic tension building mechanic that is the Jenga tower is brilliant. Forewarning: This one probably won't be so fun or even playable at all for players who have limited motor functions in their hands/arms because the only randomizing mechanic in the game is pulling blocks out of the Jenga tower without knocking it down.

I really enjoy using FATE for plenty of different genres. I played in a magic/cyberpunk/not shadowrun game, and the stunts worked really well for the magic spells second character had, and an aspect for the brain implant that allowed my first character to see magical energies. And a fantasy game I ran once it worked really well in letting my players explore character types without the strict adherance to class in D&D. And I'm using it currently for a Space Pirate game.