http://www.abandonia.com
If you can't run DOS games, though, you'll need the
DOSBox. I have problems with some of them, but quite a few of them work.
http://www.romnation.net/
You'll first need to get the emulator for the system it's on (i.e., a Gameboy emulator for Alleyway) and then download the ROM for the game and open it through the emulator.
Depending on what you want, there are other sites. But those are the best.
Cherryroms.com is good for SNES stuff (though it's down now, I think), and
CoolROM.com can be a good source for "copyrighted" games (though it does have minimal porn.)