Dungeons and Dragons

Yeah, to be honest my point is there are many good games out there. That said...

• Pathfinder: Fantasy in the classic D&D style, branched off after 3.5ed. Three action economy is gooooood once you're used to it. Lots of dice.
• Blades in the Dark: Steampunk horror fantasy. The most beautifully designed system I've played. Dice pool game that's easy to pick up and master, flavor for days, fantastic narrative control for the players and GM, easy to run. Even people who will never play Blades need to read the book, it has several concepts that can change how any GM or DM runs their games.
• Call of Cthulhu: d100 horror game about staring into the face of a cold, uncaring universe. The cashmere scarf of tabletop RPGs, just oozes luxury. The way the math on skills works is so perfectly suited to CoC's style of horror it's uncanny. Delta Green is a great variant if you want to an SCP or X-Files game.
• Savage Worlds: Action Movie! The Game. Universal system, can be used for most any genre. When it was written it was considered pretty fast to play, now it's about average. Swingy combat. I use it when I run a system not covered by other games, for me mostly 1920-1950s era detective stories. The surface level rules are intuitive, but the GM needs better system knowledge.
• Fate: Very high concept storytelling game. Players and GMs both have the ability to influence the narrative of the scene. The game I had the hardest time learning, not because of the game itself is hard but because I had to change the way I think about TTRPGs.
• Vampire: Vampires in the modern world. Dice pool system. I like the newest edition a lot, I think it's pretty elegant. Can get weird.
• GURPS: The ultimate multipurpose game. Build any character in any setting. ANY setting. Building characters is a horrible slog, but the rules are... surprisingly simple in practice, at the discretion of the GM. A lot of work in prep, but when it's right, it's very right. The Film Reroll podcast plays through movies using it, highly recommend listening to a movie run by Paulo (Home Alone, maybe) to get an idea of the system.
• Shadow of the Demon Lord: Grimdark or horror fantasy. d20 system, very easy for D&D players to learn.
• Dread: Extreme rules light horror game. Tasks are resolved with a Jenga tower. The GM creates a horror scenario. Anytime the GM wants to increase the tension or the players are in danger trying to do something, a player pulls a block (or two, or three). When the tower falls the player who knocked it over dies. Players can sacrifice their life to accomplish a heroic action by knocking over the tower intentionally. That's all the rules.
• Worlds Without Number: Fantasy. Sort of another branch off AD&D. A nicely designed mix of Old School Renaissance and some modern conveniences. Very, very good worldbuilding tools. Free, to some extent.
• Mothership: d100 sci-fi horror system, more barebones than CoC. Very easy to pick up and build characters fast, which is good, 'cause they're going to die.
• Numenera: Weird sort of futuristic/fantasy setting. One of the easiest systems I've ever run, super easy to adjust on the fly. Maybe a little too complicated to explain in a few sentences.
• Mork Borg: Old school, original D&D turned emo. Can be played straight or as satire.
• Everyone is John: A comedy game, very rules light, where the players take turns controlling the same character, John. They try to accomplish hilarious tasks. Gets weird. My John flew the USS Enterprise-D into a sun once. Free.

For people who want high fantasy but not D&D, I'd recommend Pathfinder 2e. For people who want something a little more dangerous and stripped down and are coming from D&D, Worlds Without Number. For anyone I recommend Call of Cthulhu and Dread. Everyone should read Blades in the Dark, even if they don't want to play in the setting.

Also, from the other comments below: Traveller: Space Adventures! The Game. The rumor is Firefly was based on Joss Whedon's Traveller game, and that's how Traveller plays. Amazing character creation system that lets players control some of their background, but mirrors real life in that not everything goes as planned. The setting is very, very deep. I admit I would probably play Scum and Villainy (Blades in the Dark in Space) or Stars Without Number (the predecessor to WWN) instead, but it's up there. The One Ring Roleplaying Game: Very much a system to play stories not just in Middle Earth but in the style of LotR. I have not played this and have no intent to do so, but it's clever in its own little hobbit hole way. I have read it. Cool dice.

I haven't read Shadowdark or Pugmire. Shadowdark looks, for my purposes, similar to Worlds Without Number or Shadow of the Demon Lord. As for Pugmire I use Mouseguard for my Redwall adjacent stuff, but I would sit in a few sessions for sure.