Technically not Android games, but I've got a few emus that seem to work well: nesoid, snesoid, genoid, gbcoid and gbaoid.
Lots of -oids.
These are really oudated by now though. Most can do better (especially GBA, since that was based on a PSP emulator that has better alternatives on the PSP.)
I kinda like going this way:
SNES9x EX+ (It's what is as of weeks ago the version before latest of SNES9x for free with no ads. Bingo.)
Anything with .Emu except Neo (these cost a little bit, but it's usually well worth it and it uses nice quality emulation at the core. Except for Neo, it's garbage. There are much older versions for free in the store compiled by someone else, I don't typically recommend them but...)
MyBoy (crappier accuracy for GBA but it can link cable and tilt, works better on slower machines besides. Free version has ads but the paid version costs about as much as gba.emu, blegh.)
ePSXe For Android (keep in mind, you'll be putting ISOs on your device/SD Card for this and they tend to be huge. Still this is ePSXe's latest without any plugin fuckery outside of possibly the optional hi-res plugin.)
aFBA (a few versions off by now, but it's by far the most recent arcade thing on the platform save possibly RA.)
RetroArch also covers about everything for free, but the UI's kinda meh. Plus the others tend to be better optimized depending on device. Try RA first, but I didn't end up a fan.
Oh, and uh... you'll want a gamepad for anything not turn based. Trust me. You can wing it for a few games like maybe Sonic otherwise (ePSXe's D-Pad actually ain't all that bad), but touchscreen pads in general just can't perform well.