Description
No, you don't need a license for c#. Maybe you need one for the IDE you want to use.
But there are some free and opensource IDE's out where.
You can use MonoDevelop, Webmatrix, Visual Studio Express but i suggest SharpDevelop, its open source.
sharpDevelop (short for SharpDevelop) is a free IDE for C#, VB.NET and Boo projects on Microsoft's .NET platform. It is open-source, and you can download both sourcecode and executables from this site. In addition, you can find the latest information and changes on #develop, as well as get in touch with the team in the forum.
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Update
In case of Webapplications, you need a Windows license too use IIS (Internet Information Server, Microsofts Webserver). It is also possible to run .NET on Linux, check out the Mono Project if you are interested in.