Android has a lot of great emulators, and most handhelds running the OS are the best choice for portable emulation. This guide will hopefully give you an idea of which ones are best for your device.
Keep in mind that not all emulators available on the Play Store are included in this list; some of them are nothing more than ad-supported forks of more established open-source emulator projects like nds4droid, though not all of those forks are mere ripoffs. NES.emu and GBC.emu, for example, are based on FCEUX and Gambatte respectively, yet they're decent emulators on their own right than just a copy-paste of the emulators they were based from with advertisements thrown in the side.
A relatively new DOSBox port. Despite the emulator being more obscure than the other DOSBox ports, some user reviews report better compatibility, better controls, and faster speed compared to DOSBox Turbo. v1.0.48
Decent compatibility, but Snes9x EX+ beats this in spades.
Advertises higher compatibility compared to its competition. System requirements are higher than the other emulators.
SuperRetro16 and SuperLegacy16
Formerly known as SuperGNES, though it was taken down by Google. SuperRetro16 lacks features such as box art, while SuperLegacy16 has all the features SuperGNES had. Paid versions have netplay, save state support, and other features. Free version has ads. Has CRT filters and texture scaling. Most games run fine, but audio issues are prevalent. Developers are slightly shady.
This is more of a proof-of-concept than anything. Even the most powerful mobile processors can run very few games at full speed. Most Qualcomm processors before the 810 can't run it without heavy graphics glitches due to the buggy drivers not having good support for OpenGL ES3. Working notable perfomance with somes games with NVIDIA tegra X1 with OC Dolphin option.
Very fast and highly compatible DS emulator, and might as well be your only choice for DS emulation on Android. Can run full-speed on pretty much anything it's compatible with. There's also a free 20-minute demo available.
Based off of DeSmuME. Not optimized well. Games are laughably slow, especially compared to DraStic.
*DraStic recently updated its beta build after a 9-month hiatus, so it's technically still active. Just be aware that the updates are infrequent.
This emulator has great compatibility as well as a lot of settings to mess around with. It's recommended to use the Software HD video mode, as the OpenGL plugin is very glitchy. The emulator also has a box art feature, which detected proper box art for even the most obscure games I put on it.
Compatibility is similar to the desktop versions due to the emulator being built with portability in mind, though it's obviously more demanding for mobile than it is for a desktop. If your device came out recently, it should run quite well.