A popular computer scene is emulation.
An emulator is a program that has the computer imitate a machine like an NES.

There are emulators for almost any system.
There are several good emu sites out there.

ZSNES Official Homepage

Description -

This Super Nintendo emulator is almost perfect.

Instructions -

Before playing you should configure the program.
Enable Sound and change the video mode to 640x480x256 VESA2.
If you don't support that mode you might have some transparency problems with certain games.

Here to download I have probably the best NES emu.

Nesticle v0.43
I have decided it's my favorite because the final Nesticle had sound problems and 0.42 had perfect sound but was slow.
This version has reasonably good sound and the speed of Nesticle final.

Nesticle v0.42
You can still get it here.

If you want the final version check out Emulation Excitement

Description -

Nesticle is the most popular NES emulator, I find the emulation quality pretty bad, the scrolling is pretty terrible.
What's worse is, the latest version which has a lot of problems with the sound.
This these earlier versions are more acceptable.

Instructions -

Download and unzip.
To play a game you will need a ROM.
ROMs are illegal to keep unless you have the actual cartridge.
You can find them just by searching "NES Roms" in your favorite search engine.

Legal Rom -

Here to download I have an unreleased English version of Earthbound for NES.
It was never released in the US.

Earthbound Zero (Mother)

You will need to unzip it and put it in the same directory as nesticle.

Links -

NES Land