Amiga Emulation

WinUAE was too slow to be useful on my old PC, but with a faster processor and some program updates (so it's much easier to use now), it's working really nicely. You have to get the system ROMs from somewhere, but there's a wealth of old demos and games to run, if you're feeling nostalgic.

AmigaWorld has an updated tutorial for getting WinUAE running; has a good collection of demos (even with screen captured videos, but the AVI's aren't very high quality); and Back2TheRoots has lots of games and music.

Even without an Amiga emulator though, you can play the .mod music files (which were often the best part of any demo) with CocoModX (for OS X) or Winamp. Here are some of my favourites:
Phenomena - from Enigma
Spaceballs - from State of the Art
LSD - from Jesus on E's