Here are some gba games I have found to be accessible. I'll begin specifically with boxing games, since there are quite a few of them. The very first gameboy advance game I bought was ready 2 rumble round 2. Obviously not as grand as the home console version, but for an early gba game it was pretty nice, and save for a few mini games is very playable. Wade hickstons counterpunch is kinda like punchout in terms of gameplay,, with the ability for you to unlock new moves and stat upgrades with fight money. Two Japanese exclusive boxing games based off their respective manga are also playable are hajime no ippo: the fighting, and ashita no jo. The first actually has an english dubbed anime that is more grounded in reality which I find appealing in the midst of all the other supernatural anime, in case you want to know the lore behind the game. Just look for hajime no ippo.
Transitioning to fighters, and there are quite a few of them; I will start with k1 pocket grand pre and its sequel, which are japanese exclusives. Both are ok, . Dragon ball z supersonic warriors, super street fighter 2 turbo revival, street fighter alpha 3, the king of fighters ex 1 and 2, mortal kombat deadly alliance,, mortal kombat tournament edition, zatch bel electric arena and its 2 japanese only sequels, mobile suit gundam seed and its Japanese exclusive sequel, tekken advance, guilty gear, there is also a pair of metabots games that are a combination of rpg and fighter playable with patience. Duel blades has some primitive music and no character voices but isn't too bad, BlackBelt challenge is ok, but dont bother with mortal kombat advance. And I think that's all of the fighters worth mentioning. If I missed any, please share. Also, dont forget to get the patch for street fighter 2 turbo which fixes the fatal bug in the default game which causes it to crash if you manage to make it to akuma.
Only rpgs I can think of are the main pokemon games being ruby satire and emerald, and fire red and leaf green, but like on gameboy, there are a ton of rom hacks which I wont list here simply because there are too many. Ok maybe just a couple. Pokemon ultra shiny gold, flora sky and liquid crystal are the ones I know that are complete. Also worth mentioning are riviera and ygdra union, but the psp ports are better. If anyone knows mor playable rpgs please share.
As for beat em ups, there is Jackie Chan adventures based off the cartoon of the same name, a lengthy game with some platform elements. Crouching tiger hidden dragon, same kinda thing but the first is better. X-men,: rain of apocolipse is also playable. Someone mentioned star wars episode 3. Maybe river city ransom ex. Final fight 1 is also playable, but the sound is really drowned out by the music, which may be offputting to some. Dragon ball gt transformation is also playable, I particularly like the thumping electronic soundtrack of this one, though the sounds themselves are a bit grainy. Dragon ball advanced adventure might be playable with emulator help because it has a lot of platform elements. Dynasty warriors advance is also playable, it uses a grid system which you navi through a menu to get around. There is a one piece game but I never made it very far, same with the naruto ninja council games, same with spiderman, same with guardian heroes advance. O and tmnt based off the 2007 movie is also fully playable, though the first teenage mutant ninja turtles released by konami has some platforming and vehicle stages that make it hard to recommend, and the second one is definitely not playable. Double dragon advance is also playable. And I think that covers all the playable beat em ups. If you know more, please share.
As for everything else, there is Mario party advance, wario ware inc, and wario ware twisted. Be aware though that the last game made use of a gyroscope and rumble feature which were built into the cartridge, which might make it hard to emulate. There's space channel 5, to get around the shoot buttons being either a or b, I press em both at the same time, but there are better versions of the game. Bit generations: sound voyager is very accessible, and same with rhythm tengoku. I mentioned somewhere before that there is an english patch for the game called rhythm heaven silver. What makes this entry in the rhythm heaven series stand out are its various drum challenges, and a couple minigames and toys, since many of the songs here would be reintroduced in later games for the international audience. Feela decathalon is a track and field style game that might be playable. Bleach advance is Japanese only, but is playable with patience. Game n watch gallery is the 4th game in the series and is mostly playable with emulation help. Capcom classics minimix has mighty final fight, which is a playable nes game. Activision anthology is a huge collection of over 50 atari 2600 games, many of which might be playable. And I think that wraps it up for this section.
I really wish I could find some playable puzzle games. And like before, if anyone knows more that I missed, please share. I listed my collection of playable ds games on another thread about playable 3ds games, but if there is interest, I will talk about them here. This section took about an hour and a half to write up on phone, so hope you found something useful in it.