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All the Legend of Zelda games for the GBA are rather good and I've heard Castlevania is really good too (I've never played it myself though xD). You could also play the game. Dragon Ball Z: Buu's Fury. It followed the anime almost exactly and I quite enjoyed it c:

 

There are 3 Fire Emblem games on the GBA, though one of them would require a translation patch, which can get technical. You can start the series pretty easily with either Sacred Stones or the one simply known as Fire Emblem (I like calling it Rekka no Ken, but the English name is just Fire Emblem)
Rekka no Ken is a prequel to the Japan-only game, but it's a pretty good one and holds up amazingly well as its own game. It's one of the stronger titles in the series imo.
And save states make Fire Emblem a lot easier lol

 

Advance Wars is another good one. It's made the the same people Fire Emblem is made by, so it's really similar, just with tanks and stuff instead of swords.

 

I won't speak for playing an emulator, but on pre-Advance gameboy, I really enjoyed Donkey Kong (the arcade-like one), any Kirby game on those systems, or LoZ Link's Awakening and the LoZ Oracles.

On GBA, there are two categories: original and SNES remake. In SNES remakes, I really liked Yoshi's Island and LoZ A Link to the Past, both were very good polished-editions of the originals.

As far as original games, I recommend Golden Sun, LoZ Minish Cap (which is surprisingly awesome), and, OH RIGHT, the entire gosh-darn Mega Man Zero series. That whole series of games is super tough though, so I don't recommend playing them on a keyboard. Either get the cartridges for your GBA (or the MMZ 1-4 collection on DS), or map an Xbox controller to your computer. Trust me, with all the maneuverability, reflexes, and multi-button necessary functions, it simply can't be played with a keyboard.

 

I would recommend you try out Pokémon ROM hacks such as Light Platinum. But if you don't want Pokémon, then the Legend of Zelda games might work for you. Advance Wars is also quite good especially if you have someone to play with.

 

Maybe I'm a little bit biased because of nostalgia, but if you're looking for a fun platformer, you can give Rayman 3 a try. While it's not as good as the masterpieces Origins and Legends, it's certainly a nice challenge to play on the side.

 

The Shining Force game for GBA is one of my favorites, and its good for at least 1 replay as it changes a bit the second time. Another good one for just screwing around in Pokémon Pinball. And while I'm bad at mario, i enjoy the gba Mario Party, and Super Mario 4. Another decent one is actually Pacman collection, as it has a couple intetesting twists to the normal game. The Duel Masters games are fun too in my opinion. I could probably think of more if you want.

 

I second Zelda, and add Mega Man Battle Network and Golden Sun to the list

 

I've heard good things about Golden Sun, though I've never actually played it. If you want to be a hipster you can also try Drill Dozer by Game Freak, pretty sure it has some Pokémon references in there too.

 

Golden Sun takes a bit to get going, but once it does, you'll be hooked--play the original game and The Lost Age together to experience the whole story

 

I completely forgot to add this but my favourite game for the GBA was and still is Final Fantasy VI. The soundtrack, the plot, the game-play, the characters and more made it my favourite so I recommend you play it, if you haven't played it already (or the original for the SNES(?)).

 

Join me on a quest for the sun in boktai the sun is in your hands! I'm playing a physical copy!