We need a sticky for this. For both O3DS and N3DS.
Anyways, i use O3DS so the ones i'll suggest are 100% certain to work well
genesis, snes and NES emulators by bubble (picodrive, snesx9 and virtuaNES) look up his github
for GBA either injection or GBArunner2 (haven't tried open AGB firm but people say it also works)
Deadlux64 (N64) runs, albeit slow, barely playable. I don't recommend it if you use O3DS, maybe one day it'll run better..
ScummVM for point and click adventures like monkey island works flawlessly
Gameboy and Gameboy Color, use Gameyob. Make sure to try both the 3DS and the DS versions, the latter supports super game boy borders and according to people it's better than the 3DS version for other reasons i don't understand nor really noticed.
You can also install individual retroarch cores, like gambatte for gameboy, which works slightly worse than gameyob but has more settings to fiddle with, and quickNES, which works flawlessly and.. if you don't hate retroarch you could use over bubble's virtuaNES i guess.
That's all from me, i haven't tried any older consoles emulators. the NEOGEO emulator for DS allegedly can run on 3DS but you have to go thru some shenaniganz that i didnt deem worth it. PSX doesn't boot (as far as ive tested). There's also ports of games like doom and mario64 if you dig that