[RandomHeretic]

Comment removed.

[Chronosplit]

But what you're talking about MyBoy has "crappy" accuracy?

MyBoy's fine at it's job for the most part but you'll notice it most on games like the Golden Sun duo, there are some issues like sounds don't work completely right.

*important meeting*

Boss: We need to get profits up... Wait, what are you doing!?

You: I'm trying to fight Dr. Robotnik! I mean, damn...

Boss: You're fired.

You: It won't happen again, I promise!

Boss: No... I hate Sonic!! GTFO!!!

Working at Nintendo can be strict sometimes! 

[Sliver X]

While things have come a long way in the past few years in regards to dirt cheap, somewhat powerful SoCs being prevalent note that GBA.emu requires *WAY* more power to run full speed. On my ancient Xperia Play overclocking the CPU from 1GHz to 1.6GHz isn't even enough to get 60FPS under GBA.emu, while I can underclocked to 584MHz and get full speed under MyBoy!

I would also advise using MAME4Droid Reloaded over Final Burn Alpha, as FBA tends to have shitty problems with buffer under run with sound so things get "crackly" after 30 seconds or so.

And in regards to the original question, I had fun with Chaos Rings, Bard's Tale, FF4: The After and Final Fantasy III on my phone.

[Chronosplit]

While things have come a long way in the past few years in regards to dirt cheap, somewhat powerful SoCs being prevalent note that GBA.emu requires *WAY* more power to run full speed. On my ancient Xperia Play overclocking the CPU from 1GHz to 1.6GHz isn't even enough to get 60FPS under GBA.emu, while I can underclocked to 584MHz and get full speed under MyBoy!

This is true.  I posted from the more recent end of devices, though stuff that can run the list is much more available than it used to be.

Another thing to keep in mind if you're running something reasonably older is FPSe over ePSXe.  It just might be slightly faster in spots as it has more customization options but sound may have some issues (so I wouldn't rec this otherwise).  Also, if SNES9x EX+ happens to be too slow for you, there's a version of that based on 1.43 more suited for slower devices here. (there's also sideload builds for EX+, but you should most likely use the play store unless absolutely needed.)