Here's something you need to do for the sake of reminisce:
Do a Google search for NES emulator. (I already did this for you)
[url=http://www.emulator-zone.com/doc.php/nes/]The Emulator Zone - Nintendo NES Emulators[/url]
Download one of these emulators.
Then do another Google search for a rom of any game you might want to play. Example: Dragon Warrior NES rom.
And of course, the good old Rus gives you his blessing with emu-russia, which is one of my favorite resources for emulation. Lucky for you, there is also English!
[url=http://emu-russia.net/en/roms/]Download - ROMs[/url]
Look for the NES section and to view the entire database for NES, click ALL ROMS. Find Dragon Warrior and download. You play the game by running the NES emulator and doing File>Open on the menu and selecting the ROM in its directory. It should run, but you should probably set the joystick controls before you play. It's keyboard compatible, too.
Of course there are other gaming consoles that you can emulate on a computer. You should check it out.