A great Guide to Awesome Emulators; tho, Google the Emulator's Official site as their Download maybe of an Outdated Version: http://www.freeemulator.com/
Known Current Emulator Versions (for Windows; That I Personally Use):
Legend: Console/ Emulator/ Current Version
PSP/ PPSSPP (x86)/ 0.9.9.1
PS2/ PCSX2/ 1.2.1 r5875
PSX/ pSX/ 1.13 -final
Download: pSX Emulator
N64/ Project64/ 188.8.131.52
SNES/Snes9x (x64)/ 1.53
NES/ RockNES/ 5.142 (My Personal Favorite; not listed on the site)
Download: RockNES 5.142
GBA/ VBA-M/ 1.8.0 r1229
NDS/ DeSmuME (x64)/ 0.9.10
Wii & GCN/ Dolphin (x64)/ 4.0.2
Atari 2600/ Stella/ 4.0
MS-DOS/ DOSBox/ 0.74 (Doesn't quite work on 64-Bit hosts)
As you see; I have Tried a Emulator for Almost Every Console! (Even a Semi-Working one for a Nintendo 3DS; But, I Talked about that in a previous Post)
Systems Currently without Emulators (Non-Working, Fake, Viruses, or Scams):
Microsoft Xbox 360, Microsoft Xbox One, Sony PS3, Sony PS4, Nintendo 3DS, Nintendo Wii U.
Currently "Homebrew Only" Projects:
Nintendo 3DS/ Citra
Sony PS3/ rpcs3
Microsoft Xbox 360/ Xenia
Graphics rendering with Emulators; for Windows mostly use DirectX (Usually Direct3D or Direct Draw); Tho, you can also get decent Graphics with OpenGL. And, certain Emulators are powered by OpenGL only. And you'll find that XAudio2 will work better than Direct Sound.
It's also common to Use a Gamepad with Many Emulators as Well.
My Gamepad is an PDP Afterglow AX.1 Xbox 360 USB Controller.
Snes9x 1.53 GTK Deb Install Packages (.deb):
These PPA Packages for Linux Ubuntu 13.10 "Saucy Salamander"; Tho, the Deb Packages will work with any "Modern" Distribution that can use the "GDebi" Package Installer. I installed the 32-Bit Version under Linux Mint 16. (Downloads Listed here Because they are hard to Find; and the Ubuntu/Mint version in the Software Center is Outdated.)