I'm not big into RPGs, so I'll leave that to everyone else here.
Action:
-Gunstar Super Heroes- Awesome sequel to the Genesis classic. Well-done all around; I'm not a big fan of the overhead shooting stage, however.
-Astroboy: The Omega Factor- Like GSH, Astroboy is an incredibly well done action/shooting game from Treasure.
-Advance Guardian Heroes- I have a love/hate relationship with this game...it's NOWHERE near as good as Guardian Heroes was, but it's also a very different game, is very challenging, and has great replay value.
-Double Dragon Advance- The best classic-style beat-em-up game released this generation, period. An excellent recreation of the orginal arcade game, with new stages/enemies from DD2, and moves taken from every game in the series. A must-buy if you like the genre.
Fighting:
-Street Fighter Alpha 3 Upper- Still an impressive port of the game to the GBA; certainly not perfect, but developer Crawfish managed to squeeze in the entire roster, plus Yun, Eagle, and Maki from CvS2, into the game, along with a large amount of voices, all the ISMs, and even dramatic battle modes. Some of the characters even have animations missing from the PSX port of the game.
-The King of Fighters EX2- The first EX game sucked, but the sequel plays almost exactly like KOF 2000. The roster is a little on the small side for a KOF game, but it plays very well and has three new characters.
-Guilty Gear X Advance Edition- Doesn't look as good as the other two fighters, but plays great and animates very well. The game even has team battle and tag battle modes that the other GG games are still lacking in.
Platform:
-Dragonball Advance Adventure (import)- Well-done platformer based on the original (as in Goku as a child; no Z drag-on battles here) Dragonball story. Some boss fights are done fighting game-style, and the game play mimics the battles from the series, with air combos and huge fireballs.
-Mario Advance series- You pretty much know what to expect here.
Puzzle:
-Super Puzzle Fighter II Turbo- Has a bit of a bad reputation of the GBA due to some bugs; my copy has never crashed, but a lot of people have had the game's memory get erased for no reason whatsoever. Despite this bug, Puzzle Fighter is a great port overall.
-Panel De Pon/Dr. Mario (import)- This recent release contains two great puzzle games in one cart, for about $20. Definitely worth it.
Adventure:
-Castlevania: Aria Of Sorrow- The other two GBA Castlevania games are good too, but AoS approaches the same level of quality as SOTN. A must-buy.
-Metroid Zero Mission- Awesome remake of the original Metroid with more areas to explore than the original game.
-The Legend of Zelda: LttP- Great port of the SNES classic.
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The Legend of Zelda: The Minish Cap- I'm currently playing through this game right now...it may end up beating out Link's Awakening as my favorite GB Zelda game.
-Shining Soul II- Fun dungeon crawler with a variety of characters to play as. I sold this off a while back and I really miss it right now.
Racing:
-Mario Kart Super Circuit- Not only does the game have a bunch of brand new stages, but you also get all the classic courses from the original SNES game!
-F-Zero Final (import...I think this is the right name)- The third F-Zero GBA game; contains some challenging courses, a large number of cars, and a track editor(!).