Recommended emulators

All links here will take you to the latest build of that emulator, if you what more info regarding the emulators, either check the Emulators page, or use Google.

NES/Famicon

General: Nestopia

Accuracy: puNES or Nintedulator

SNES/Super Famicon

General: Snes9x

Accuracy: higan/bsnes

(I'd recommend using bsnes core in RetroArch to get around some less-user friendly implementations of bsnes)

Nintendo 64

Accuracy: Mupen64plus

Really N64 emulation is a mess, I'd actually recommend checking out this site and using the appropriate emulator/plugin per game.

GameCube/Wii

Dolphin

GameBoy/Color/Advance

General: VisualBoy Advance-M

Accuracy:Gambatte (only emulates GameBoy and GameBoy Color)

NDS

DeSmuMe  

Playstation

General: PCSX-Reloaded

Accuracy: Xebra or Mednafen

Playstation 2

PCSX2

PSP

General: jPCSP

Up-and-coming: PPSSPP  

Master System/Genesis

Kega Fusion

Saturn

SSF

DreamCast

nullDC

DOS

DOSBox

Multi-System

RetroArch