NES: Nestopia UE core without a doubt, its the best and most cycle accurate emulator, it plays all official games released and excellent famicom disk support. FceuGX for lightgun (zapper) games, Fceumm core for those weird nes hacks or modified mappers.
SNES: Snes9x Next core if you want better SFX emulation and 97-99% accurate sound. Snes9x GX for super scope games and the likes. Some Virtual Console snes games run better than with these emulators.
GB/GBC: Gambatte core, another perfect example of a cycle accurate emu. It has custom palette support and sgb/custom borders when using overlay settings. There's no point to use vba gx anymore.
GBA: mGBA core, the best you will find for GBA emulation on the Wii. Another BIG reason to leave vba gx in the past.
to be continued...