F-Zero GX: It's been over 20 years since the GOAT dropped and all we've had to show for it is that damn 99 game. Go play this and weep that we'll never see another like it.
Nintendo Puzzle Collection: The best version of Panel de Pon, but SNES is a close second if you wanna play on a device that can't run Dolphin. GBC is also kinda noteworthy for having a unique singleplayer to work around platform limitations - opponents have a lifebar rather than a board. Just don't bother with 64.
Tales of Symphonia: This game got a PS2 rerelease with some extra content, and the HD remasters are based on that version. But the catch is that they were downgraded to 30fps, and yes that includes the so-called remaster. So I still recommend playing the Gamecube original at 60.
Wii:
Puyo Puyo 20th Anniversary: The absolute pinnacle of the series (by which I mean it's all downhill from here, I will never forgive Sega for what came next ), crammed with a whopping 20 game modes. I really love the challenges where you have to chain under bizarre restrictions. I prefer the Wii version for its 480p assets, and it's the easiest to emulate, but if you care about story mode the translation patch only exists for DS.
GBC:
Game & Watch Gallery 2: Holds a special place in my heart as the first game I ever owned. Has the best lineup out of all the collections, with 3 and 4 you can kinda tell they had used up all the heavy hitters.
Mario Tennis: An incredible tennis RPG. And Mario doesn't even show up until the postgame as a bonus boss, which I find hilarious. Has connectivity with the N64 version if you can get that running, lets you transfer your RPG mode character and unlock more content on both titles.
GBA:
Boktai series: These games were so near and dear to my childhood, especially 2. Really though you want the Solar Sensor hardware for the full experience, but I love these games too much not to plug them anyway. Emulating them is worth it over not playing them at all. And for the third game, you'd have to pick between original hardware or the translation patch anyway.
Golden Sun 1/2: These games were way ahead of their time for how they designed a combat system that encourages you to use all of your tools and not just click basic Attack as if you gotta hoard your MP for a rainy day. Fantastic puzzles too.
Mother 3: Surely you have already heard of this game and do not need me to tell you to go play it. Have you not played it by now? Why not? Well, okay, if you haven't played Earthbound first, go do so, then play this.
Rhythm Tengoku: A wonderful game about pressing the A button. Sometimes you press the d-pad too. Translation patch.
Summon Night: Swordcraft Story 1/2: If you've ever played the classic 2D Tales games, these are excellent spiritual successors to those. There's a third game that's JP-only, translation patch is being worked on but it's been stuck in development hell for years...
Romhacks:
Celeste Mario's Zap & Dash (NES): SMB1 turned into a Metroidvania with Celeste mechanics ported in. I think what impresses me the most is that they got 4-directional scrolling into this engine.
Super Metroid and A Link to the Past Crossover Randomizer (SNES): It's an absolutely incredible technical feat that this even works. SM and ALttP smashed together into a single ROM, with a few doors that take you from one game to the other, then the item pools are shuffled together so you have to go back and forth to find one game's items in the other. Unfortunately because ALttP is a much bigger game with a lot more items it kinda overshadows SM, you may not find this to be as replayable as the standalone randos. But I recommend trying it once because it's just so cool the first time.