I guess it is time for me to update my recommendations, it's been several years.
I will still generally recommend using Retroarch when it has an available core for a system you want to emulate just for the simple objective fact it has lower input latency with adjusted frame delay and if you want to fiddle around with it, run ahead. It also has lower audio latency, you just need to adjust it as much as your CPU will allow. While not objectively a reason to use RA over stand alones shaders are a great subjective reason to use it, there are amazing looking CRT shaders available. Another great reason to use RA over most stand alone emulators is the ability to setup custom settings and controller mappings on a per game basis
Now for the list:
NES - Mesen is still king, RA or stand alone
SNES - Snes9x, Higan and BSnes are all very good and you won't go wrong with either. I still prefer Snes9x just for the performance alone, you can really push the frame delay in RA with it
Gameboy Advance - mGBA, RA or stand alone
Gameboy / Gameboy Colour - Sameboy, RA or stand alone
Gamecube / Wii - Dolphin standalone, the RA core still is no where near as good
Nintendo 64 - Mupen64plus, RA or stand alone. While PJ64 is a good emulator its nag screen garbage is awful
Sega Genesis / CD / Master System - RA with the GenesisGX core is the only real choice here, all other options have severe issues
Sega Saturn - Mednafen, RA or stand alone
Sega Dreamcast - Flycast or Redream, both are excellent
Sony Playstation - Mednafen and Duckstation are both great and equally good, use either the RA cores or stand alone options
Sony Playstation 2 - PCSX2 is the only choice here, use the stand alone over the RA core
Sony PSP - PPSSPP, use the stand alone over the RA core
Arcade - Mame stand alone, avoid the RA core, it messes with controls too much
NeoGeo - Mame stand alone or the FBN core in RA
Turbografx 16 / CD - RA or stand alone Mednafen
Atari 2600 - Stella RA or stand alone
Atari 7800 - A7800 which is a fork of Mame with everything else stripped out and adds extras
Atari 5200 - this is a tough one but I will recommend Kat5200 for its overall general ease of use without sacrificing quality