ZSNES is a fast open-source emulator originally developed for DOS, but later ported to Windows, Linux, *BSD, BeOS, and Mac OS X (Intel). Being written primarily in x86 assembly, it is one of the fastest emulators available. It will run fine on a 200 MHz machine. Today, ZSNES is considered to have the most wide support for special-chip hardware and possesses some of the highest game compatibility around.
Snes9x is a portable freeware emulator. In some form or another, Snes9x has been ported to Linux, PowerPC, PSP, Xbox, GP2X, and others. The source code for Snes9x is publicly accessible.
Higan (formerly bsnes) is an open-source emulator for Windows and Linux. Its primary focus is accuracy and as such it might be the most accurate SNES emulator currently around. The system requirements for achieving full speed are however quite high (somewhere in the area of 2GHz). For those who want their games to run on the actual SNES console, bsnes should be considered
SNEeSe's primary goal is that of accuracy. It was originally developed for DOS, but is now primarily for MS Windows. SNEeSe uses the Allegro library, and has unmaintained ports to Linux and BeOS. In the future SNEeSe may serve as a testbed for advanced ideas having to do with accurate synchronization.
Super Sleuth is an closed-source debugging emulator exclusively for Windows 95/98/ME.