UAE Amiga Emulator
The first Amiga "emulation" is a hoax program for MSDOS that displays the "hand holding a disk" picture used in old Amiga ROMs and tortures the floppy stepper motor a bit. You can download this hoax program, but we make no guarantees that it does no harm to your system. It could be a virus (it's probably safe, but I haven't disassembled the thing, and it's a bit large for a GIF viewer. This isn't quite the original: for copyright reasons the Kickstart 1.2 ROM which was contained in the EXE file was removed. It runs fine even without it ;-)

After that, a very nicely done GIF file appeared: NXAmiga.gif, which is also a hoax, but a much better one.

Then came UAE...

These days, UAE is no longer alone in the world. It now has a fellow: Fellow, which is another Amiga emulation written by Petter Schau. As it seems, Fellow is now maintained by Dominik Schmidt and Torsten Giebl.

Like UAE, Fellow has been ported to other platforms. Get the Windows port of Fellow. More information can be found on the WinFellow homepage.

There's a port of Fellow to Unix based platforms using X11 from Riot777. Have a look at xfellow.sf.net.