First, back up your games on your PC with Game Copy Pro (dvdwizardpro.com). You can burn a title to another CD or DVD, or just keep the ripped file on your hard drive. The handy utility tackles Xbox, PSOne, PS2, Dreamcast, Gameboy and GBA.
Next you'll need an emulator, which lets you play the ripped game on your computer. Emulator-zone.com has a comprehensive selection of emulators for most consoles, from the Atari 2600 to Xbox, and often there are versions for Windows, Mac or Linux systems. Just remember that these are all amateur apps. If one seems too buggy, try another.