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M.A.M.E
This is the BIG one!! Arcade emulation extraordinaire with support for thousands of arcade games from Space Invaders to Zaxxon, from Defender to Street Fighter and everything else in between. All in care about is that it runs my favorite arcade game of all time Jackal with nary a glitch in sight!! Fabulous!!
Retroarch
This is an all-in-one multi-system emulator utilising a front end not unlike the PlayStation. Incorporates lots of emulation engines making it easy to get going but some do require fiddling around (Atari 500) with to get working correctly and some are not as capable as their standalone brethren. On the plus side they may support features not found on standalone emulators (CHD image support for example) so if you are into a into a one-stop shop type solution give it a go!!
PPSSPP Emulator
Want to play PlayStation Portable games on your PC and in high definition? If yes this is all you need. Really nice compatibility and no need to provide a BIOS makes for an easy setup. Controller support includes Xbox controllers for the PC, pretty much anything that you can use in Windows really!!
Dolphin Emulator
The best Wii/Gamecube emulator in existence with support for the Wii controller/nunchuk and even the Mayflash W010 Wireless Dolphinbar all of which makes for playing Wii games as if you are using a Wii console except everything is in high definition. Oh, and Gamecube gaming us almost perfect. Brilliant!!