I have been coding using Visual Studio 2005, in VB.NET for a while. No problems.
Recently, I decided I wanted to start a New C# project. Upon attempting to do this, I noticed Visual Studio 2005 was missing this functionality entirely!
This is exactly what I get on my screen:

(source: googlepages.com)
Also note that I have both Visual Studio 2003 and 2005 installed on the same machine. Visual Studio 2003 has the C# templates available.
Any idea what I can do to solve this issue, without a re-install?
I think you did not include C# durting the time of installation? Restart the installation and add C# to it.