Almost every computer can be emulated, and the most convenient way of using these machines are through emulators on the PC. Of course to use the software you must legally own the original, or have permission from the copyright holder to use it. Both the BBC and Amiga also require the OS ROMs which are not available as standard with the emulators and can be hard to find.

Here are some links to the best sites for getting hold of the emulators, and the software to run on them.

BBC Micro/Electron

BBC Lives! - The best place to start looking for BBC Emulation stuff. Include a massive file archive of downloadable games. Sadly Superior Software are still exercising copyright of their own (and Acornsoft) games. Superior made most of the best games (Repton, Citadel, Exile) so you'll need to go hunting to find them as they are not part of the archive.
BeebEm - Home of the best free BBC Emulator.
ElectrEm: Acorn Electron Emulator Page - Electron Emulator!
Stairway to Hell - Probably the best BBC/Electron gaming resource.
Superior Interactive - Superior still exists: remaking all the classic BBC games for the PC (for a price).

Sinclair Spectrum

World of Spectrum - The Best place to start is you are a Spectrum fan.
Sinclair Research Ltd. - See what Sir Clive is up to now.

Commodore 64

Lemon - Probably one of the best sites for C64 stuff.
C64.com - Another games site to keep you going.

Commodore Amiga

WinUAE Homepage - The Fastest and slickest Amiga Emulator available. Run most games perfectly.
Amiga Forever - The legal way to get hold of the Amiga ROMs and OS.
Amiga Inc. - Find out what Amiga Inc. are up to.
WinFellow Homepage - Another Amiga emulator. Development has stopped so not much point due to WinUAE.
Back 2 the Roots - Good Amiga resouce, with games to download.
AmigaInABox - Install into the WinUAE folder and have a number of preconfigured Amigas. Bit out of date now.
Amiga Emulation Nation - Includes ftp archive of Amiga games.
Classic Amiga - Amiga info.