Steem is an open source Atari STE emulator for Windows and Linux. It runs almost every ST program ever made without any problems.
The TOS Firmware (listed below) is required to run the emulator.
SainT is a Windows based cycle accurate ATARI-ST emulator, written by James Boulton and Arnaud Carre.
Hatari is an Atari ST/STE/TT/Falcon emulator for GNU/Linux, BSD, Mac OS X, Windows and other systems which are supported by the SDL library.
Hataroid is an (in development) Android port of the open source Atari ST / STE and Atari Falcon emulator Hatari.