The Super Nintendo was a late-comer, the Sega Genesis/Megadrive was already out for 2 years, and had a big following. Nintendo needed something to draw those people away and get their NES users to switch over to SNES. It was an instant hit, with a lot of special graphics chips and sound chips. It had crystal clear pictures and sound, something the Genesis lacked. Streetfighter 2, Super Mario World and F-Zero were enough to convince people. The SNES did extremly well, and rightfully so.

  Zsnes 0.988 - DOS (ZSNES Site)
  Zsnes 0.988a - DOS 100% ASM version of ZSNES, lacks DSP support and netplay.
ZSNES is an AWESOME piece of coding, which is why this is the preferred SNES emulator for most people. It has unbelievable speed and sound, DSP support (Mario Kart works!), partial Super-FX support and 16bit gfx support.

  SNES9x 1.16a - DOS without GUI (homepage)
  SNES9x 1.26b - DOS with GUI
  SNES9x 1.29 - Windows
  SNES9x 1.20 - Windows/3DFX
  SNES9x 1.19 - MAC (if files are needed, check www.emulation.net)
  SNES9x 1.19/i386/c6lib - Linux
  SNES9x 1.26 SOURCE CODE!
SNES9x is the MAME of SNES gaming. It has open source and is ported to about a dozen platforms, even to the Nintendo64! It has an extremely big compatibility rate and is pretty fast. It can do a lot of the things ZSNES can, including DSP support. For more ports, please visit the SNES9x Site!

  NLKE 0.04b - DOS
This is a product of 2 merged SNES emus (NLKSNES and ESNES), combining the best of both worlds. It has the speed of NLKSNES and the sound of ESNES.

  SNEeSe 0.371 - DOS (SNEeSe Site)
This emulator has risen from its grave and is now updated almost every week. A very competent SNES emulator and one to keep an eye on. The source code is available at the homepage.