If you are found of playing T.V. based Nintendo console cassette games on your computer then, you must check out the services offered by PlayNes and Nintendo8. These sites offer you to play Nintendo games online without a need of installing any Emulator to your computer. So, this gives an advantage to Linux or Mac users, for which there are less number of Emulators available.
I enjoy playing console based games online when I get free time, these games are light on system resources and have good background music. Some of the NES based games, which I like the most are- Nintendo8 provides a wide variety of gaming categories, these include action, adventure, arcade, fighting, rpg, racing, sports, etc. It also supports GBA , DOS based games to play online, it also requires Java Runtime Environment to be installed. Related Articles:- 
An updated version of Java is required to play above games, you can download Java Runtime Environment from official site of java here . Just select your operating system and install JRE to play NES based games. You can also save the state of game and can play it latter on at PlayNES.
There is a new website not requiring to play with Java, but with Flash it's called Goldies Games they have NES, Genesis, Sega, and TurboGrafx 16. Plus a few arcade coin op games, many games every week.
Check it out : http://www.goldiesgames.com
Love concole games