Update! (11/30/2014) Running Netflix in Linux is much easier. More or less, if you have Google Chrome 37 or more, it should run out of the box. Chromium did not work for me but pure breed Chrome did. This just made Linux users lives easier!
Source: http://www.omgubuntu.co.uk/2014/08/netflix-linux-html5-support-plugins
Netflix requires players to use DRM so that they can prevent downloading of videos from Netflix. On Windows, Microsoft Siverlight is used and is run in whatever browser you use. If you try to do the same on Linux though, you will find out that there is no straightforward way to play Netflix. You will be able to see Netflix’s site and manage your Queue, but you cannot play the video. Well, most Linux users with Netflix want to be able to watch Netflix on their computers.
The first approach was to install Netflix Desktop. This was a Firefox browser running on Wine. In my experience, it was choppy and took up too much memory for my liking. It worked for me but I would consider it deprecated now.
The current approach is to use Pipelight. This method is more logical: it installs a Silverlight plug-in into your browser. This way you can go straight to Netflix in your browser and do nothing special when you are in Linux. The install directions are below and were very easy and simple. From my experience it works very well too.
Sources:
Man and Keyboard 