Wow. Now this is a big question! I’ll just mention a handful of “hidden” gem kind of games, brought to life thanks to the power of emulation. just in case everyone mentions the same things.
JRPG games are always fun. But when they’re in Japanese only, they aren’t always easy to play. Enter the world of translation patches. Back in the early emulation days, there were three excellent games that were translated:
Seiken Densetsu 3 (trials of mana)
Tales of Phantasia
Star Ocean
These three games on the Super Nintendo are probably the most taxing games to emulate, weighing in at 48Mbits. Ie, 6MB lol. Huge for the day. They were also the hardest games to emulate correctly, with compressed textures/fonts, extensive voice recording and onboard chips. Not only did they push the SNES console. They pushed the emulation scene. They are a treat both visually and audibally, and have what has paved the way to be the format and plot trope for many games today.
(Tales of phantasia was also translated excellently for the PlayStation, but we’re just talking Nintendo atm)
On the side of more of a retro revival, the NES gave birth to the Castlevania series; as seen on Netflix ™.
They were excellent games, however one stood out in particular. Castlevania III, or more succinctly, Akumajō Densetsu. The Japanese version in particular had an extra hardware audio processor built into the cartridge, allowing extra levels of audio, and a much deeper bass. For a while I thought that we would never get to hear this, emulated. I was wrong. Emulators now can process the extra levels of depth, and we can experience it! Your ears will be treated to some amazing music that you would be hard pressed to believe was on the NES.
In addition, there were some differences in the Japanese version compared to English. For some reason, they decided to jack up the difficulty of the English game to 11. Some people like that. Others find it frustrating. Basically, you were squishier, and couldn’t hit as hard. One character in particular was meant to throw swords across the stage while climbing on walls.
The English version decides to effectively equip him with a butter knife. Nowhere near as cool or fun. The colour was better imho in the Japanese release, however the one thing that was lacking was being able to understand. There is enough dialogue in the game to be worth reading. You get to meet Sypha, the female speaker from the Netflix series. The English version had the translation, as well as a more gothic font to match the game.
A lot of anti Christian references were removed from the western releases, including an entire weapon! The flying boomerang like crucifix is my favourite weapon in the game. The English version replaces this with an axe. It wasn’t just a sprite redraw. It worked completely different, with an arcing trajectory instead of a horizontal returning path. The opening splash screen also has less fancy embellishments on the large crucifix that Simon (of Ralph as he’s know in Japanese) is seen kneeling before.
Thanks to emulation and patching, a special amalgamation of the two games was made, taking the best of both worlds. I would highly recommend getting a hold of this game if you enjoy 8bit classic games. The speaker of the gameshell does the game justice, and the naturally staggered pixels of the gameshell gives the low resolution pixel art some extra depth, akin to scan lines.
For me, I can’t think of Castlevania without also thinking of Mega Man, or Rock Man as he’s known in Japan. Another game that saw a lot of breakthrough in the emulation scene is Rock Man and Forte. Later on it was officially translated to Mega Man and Bass. It took a much different approach to the Mega Man X series on the SNES, which was also excellent, but a lot darker. Rock Man and Forte had a much brighter palette, and a much more cartoon like animated theme, while maintaining more of the classic old school level design and boss fight mechanics. In the early emulation days, this was a tricky game to emulate, often resulting in garbled textures and hanging boot screens. This now runs perfectly on any snes emulator on the gameshell.
The translation patch made also translated the entire database, and even has the option to “regionalise” it to the western name shuffle conventions. Ie,
Rock Man = Mega Man
Blues = Proto Man
Forte = Bass
Or you can just keep the Japanese names 
Mega man and Castlevania were the two games I played the most on my NES and game boy as a kid growing up. They hold the most nostalgic value. Another series that is synonymous with nintendo is Zelda. I won’t go into all of them, but make a special mention of the DS games: the Phantom Hourglass and Spirit Tracks. These two games in particular were great, however had a hand cramping horrible forced control scheme, using purely the touch screen and stylus to control Link. Thank god for patches. A patch was released to allow you to control link with the dpad and ABXY buttons, like a normal game. This makes it playable on the gameshell as well, seeing as we don’t have a touch screen yet. It is a far more enjoyable experience in my opinion, using this control scheme. In addition, the gameshell actually emulates the Ds very well!
Speaking of DS games emulated and translated well, Nino Kuni was actually originally a Ds game! The recent ones that came out on PS3, and later remastered for PS4 and switch were essentially the DS game for the first part, then contained completely new chapters to chronicle the wrath of the white witch. This is like playing a studio ghibli movie mixed with a Pokémon like action rpg. I think this may be the largest game on the Nintendo DS. The physical release requires you to have a physical spell book on hand to refer to different spell runes that you need to draw with the stylus, so have that handy as a PDF on your phone. Also, you will need to modify the arduino/keyboard of the gameshell to allow the mouse mod to let you emulate the touchscreen properly.
On the GBA, Mother 3, otherwise known as Earthbound 2(?) was another game that never made it to the west, no doubt due to copyright violations from sampled audio. It is an extremely quirky, emotional and unique jrpgs of the time, paving the way and being an inspiration for game’s such as undertale and other similarly self aware games. There was a translation patch that was made that is very complete, and also very good! Now you can play the story featuring Lucas, as seen in Smash Bros.
On that note, Mother on the NES, otherwise known as Earthbound Beginnings/Zero is definitely worth playing. There was a big hoo har regarding a secret internal English translation prototype that Nintendo never released, and ensuing controversy whether or not the fan translation was in fact based on this or not. Or something like that. It was a big thing in the emulation scene. So nowadays you can either play the original NES version, or try the GBA translated Mother 1+2 port. One thing you will realise is that the game is stupidly hard. There was a patch to make it easier, if you just want to get through the story. Debatably, some people don’t like how the audio has been updated on the GBA and prefer the original NES audio. Personal choice, really. Just like Final Fantasy, the naming conventions of the game is silly. So to put your mind to ease, Earthbound is the same as Mother 2.
I will just leave it at that for now, before I end up writing an entire thesis. The purpose of mentioning these in particular are for making a note of the most historically amazing games that were made better thanks to emulation. It was a case of fan made improvements to the game to make them accessible to a much wider audience, both due to regionalisation and rareness. I also tried to steer clear from things that other people would mention, to give a bit more variety, and also to give you a taste of how far you can push the gameshell.
I won’t be able to provide download links, but they should be easy enough to find.
Re: audio distortion in mgba, I have set it to only GBC and GB games on my gameshell. In general, I prefer to use GPSP for GBA emulation. If you’re using my gameshell image, try changing the kernel to the stock 5.3.6, clockspeed to 1008MHz and setting silent boot from within the utils folder. I had problems, not with audio; but strange jaggy staggered movement with the standalone gpsp and Mother 3 when using any newer kernels. It was fine in Retroarch however. I’m not sure which game you are playing, but see if that helps the audio.