Emulators

Emulators will allow you to play stuff from gaming console or other smaller stuff on your laptop, pc or phone. Think of it being like a Virtual Machine, in the shape of a SNES or a PS2. Nowadays most phones can run Playstation 1 and PSP type stuff with a little tweaking to the settings!
Below you'll find links to various emulators I use or used for both computer and (mostly) android phones.

All in 1 - Android

GBA - Android
GBC - Android
NEO GEO - Android
N64 - Android
DS - Android
GC - Android
NES - Android
DREAMCAST - Android
SEGA SATURN - Android
PSX - Android
PS2 - Android
PSP - Android
SNES - Android

To run most emulators, you will need a BIOS File. Legally I cannot be seen throwing those out there, but these are not terribly hard to find.

ROM's

A ROM is simply the game file. Sometimes the company that published or produced the games will go on an internet hunt to kill as many ROM sites as possible. Always look around a bit yourself! You never know when a site gets nuked to quickly stop legal devastation. USB drives are your friends.

Coolrom

Zophar's Domain

Sony ISOs