The answer is yes, and its possible through emulators.
The emulators themselves aren't illiegal, as long as you own the original console, and the ROMS aren't illiegal either (supposedly), as long as you have the original games, but its a touchy subject.
Many emulators are around, including ones that can play all the old systems, including Snes, Megadrive (Genesis), PS1, N64, but, when it comes to new consoles, no ones really managed it yet.
So no, you won't find a Wii emulator I don't think, that plays commerical games for a while, and as far as I know, there isn't a working Xbox 360, or PS3 one either.
You have to make sure you know what you are doing though, and read up on the emulators first before even attempting to run one, as many are fakes that I've encountered.