Buncha youngins with your GBAs.

My favourite OG gameboy game was Kirby's Dream Land. Played and replayed it many times. Even had one of those attachments to magnify it and light up the screen when it got dark :)

The Megaman Battle Network series on GBA is awesome. Replayed a few of them last year and they are still great.

Tetris change my mind

The non-pokemon ones I played the most were:

DMG: Kirby's Dreamland 2

GBC: Shante

GBA: Drilldozer

Platformers to me always felt like the best suited games to handheld games, and I love the bright colorful art styles. Drilldozer is definitely my all time favorite. If you can find a copy, I'd highly recommend it! The rumble pack cartridge is so cool.

I was also going to say MMBN, but since that's been said, I'll say Golden Sun. Loved both of those games to death.

Breath of Fire 1 and 2 are also great (although technically SNES ports).

I really enjoyed Kirby and the Amazing Mirror

Never sleep on Wario land

I know you mentioned Zelda, but there were actually a ton of pretty good Zelda games like Oracle of Ages/Seasons. Advance Wars was pretty fun. Golden Sun too. I also have to agree with MMBN from the other commenters.

Golden Sun GBA. GBC, Wacky Racers and GB it was Tetris because I had nothing else, lol.

Metroid II: Samus Returns & Gargoyles Quest (such a bloody hard game) on the OG GameBoy were my favs. I played a lot of *Battletoads *on it too but that game was so bloody frustratingly difficult, especially for a kid, so played it mostly out of spite to get past the stupid brain ball chasing you level. Also loved Parodius (parody side scrolling SHUMP from Konami) but never owned it, so borrowed it from friends to play. Naturally I also played Tetris to the point that the music still haunts my dreams. There was also a pretty decent Spider-Man game for it, but can't remember it's name & it's not showing up on lists.

The OG GB also had a lot of bog awful licensed property (movie/tv/cartoon) tie in games too, as well as generally terrible releases. To see them all, check this list: https://en.wikipedia.org/wiki/List_of_Game_Boy_games

I unfortunately never owned an Advance, so only got into games on it later via official emulators (the Wii U control pad was the best GB Advance out there), so got to play Golden Sun later but enjoyed it as a fairly unique take on the J-RPG genre.

For GBA games, here's a list but so many shitty licensed games there too: https://en.wikipedia.org/wiki/List_of_Game_Boy_Advance_games

Wario land, Metroid 2, Donkey Kong 94 are all great

If you're playing Gameboy specifically, and not including Advanced, then I played a ton of Marble Madness. I never beat it, but it is pretty fun physics-y platformer.

If you are including Advanced, then Metroid Fusion is a classic. Atmospheric, and beautiful sprite work. Genuinely scary in parts, and leads right into Dread if you like the gameplay.

Not exactly my favorite (because we already know Pokémon is) but I do remember playing Tetris a lot. My mom had bought one of the giant grey Gameboys with black & white display in the early 90's and that thing lasted as long as any of the other handhelds we got throughout the years.

Dragon Warrior Monsters for the Gameboy Color was fantastic. It was somewhat similar to pokemon, but had some features that pokemon didn't get for several iterations, like having your monsters follow you around, monster breeding, and multi-monster fighting.

Magi Nation was also good, similar vein to both of them, but felt darker in tone. Although maybe that's just how it seemed to a much younger me.

Kingdom Hearts: Chain of Memories. Has to be one of the best GBA games made

Does Yoshi's Island count? I loved that game to death and it's ending makes me tear up as well.

I will never not shill advance wars 1 and 2 Great gameplay, great artstyle, great everyting

I played thru Kirby about 3 times I. A road trip from California to Texas so I'll go with that

I was given a copy of Azure Dreams for the Gameboy Color, this thing had no picture on the cartridge anymore and was a piece of paper with the word Azure Dreams written on it. I remember playing the absolute shit out of that game. I still have it, but haven’t played it in decades.

I would recommend that you check out Golden Sun.

Kirby's block ball was a great Gameboy game. I remember one I liked a lot called lock n' chase, name could be wrong but I'm sure it's close

@NoHardshipInPancakes Link's Awakening is still my favorite game of all time. I got stuck on the second dungeon for literal years because I didn't put together that you had to defeat enemies in a specific order to get the boss key. That was way before the Internet had every answer to every question. 😋

Advance Wars for GBA was up there for me (below any Zelda game). I've got my eyes on the Switch remake, but holding until I can find it on sale.

One game I never see get talked about it daedalian opus on the original game boy, I used to love that little puzzle game when I was young. I wonder if it would hold up haha.

Advance Wars

Monster Max. It's an isometric exploration platformer/puzzle game with a rock'n'roll theme that I absolutely adored as a kid. It was only released in Europe, so it might be interesting to all you US guys 😁

Tail 'Gator is my hidden gem OG GB game, fun platformer with a great soundtrack.

Final Fantasy Tactics Advance GBA, Links Awakening OG Gameboy

• Metroid II is one of my favorite games of all time.
• Mega Man: Dr. Wily's Revenge and Operation C are both highly polished and fun, but quite challenging.
• Teenage Mutant Ninja Turtles: Fall of the Foot Clan is a relatively easy, short, polished action game.
• Kirby's Dream Land is my favorite game in the series. And if you think it's too easy, turn on Extra Game mode. It will wreck you, I promise. ;)
• Ninja Gaiden Shadow and Castlevania II: Belmont's Revenge are amazingly polished challenging but fair action games.

Every game I mentioned has excellent music, is an original game (not a port), and I have played in their entirety again and again throughout the years.

Let me know if you're looking for a genre other than an action game. XD

Advance Wars.

The ~~Pokemon~~ Trading Card Game

But for real, the Harry Potter early year games were so addictive to younger me. Haven't tried a replay with them. Also thoroughly enjoyed the Star Wars Podracing game. Simple, frustrating but you get good eventually. Lastly, Mario and Luigi Superstar Saga (hopefully this is the correct game). Got it from a cousin one summer and couldn't put it down.