If you want to be part of the emulation gamers out there there's no better place to start.
For those that don't know, Emulation = copying what something else does. In other words, your computer is "copying" what another system does, like play gameboy.
There's only one golden rule when it comes to emulation:
DO NOT ASK FOR GAMES OR WHERE TO GET THEM. Google is your friend pal.
On to the websites.
Dolphin - Gamecube/Wii*
Visualboy Advance - Gameboy/Advance
NO$GBA - DS/GBA Link Cable Emulator
ePSXe - Playstation
PCSX2 - Playstation 2*
*Don't expect perfect gameplay unless you have one of the best PCs or Macs out there.