Is it possible to install a C# compiler without Visual Studio?

Sure, the framework includes a compiler, csc.exe. Look at this article for a quick how-to. The important parts:

You can get the command-line compiler (csc.exe) from Microsoft site http://msdn2.microsoft.com/en-us/netframework/aa731542.aspx.

Download the redistributable package of the .NET Framework, which includes the compiler and the .NET Framework with C# 2005 syntax support.

The compiler is located in the following directory: %windir%\Microsoft.NET\Framework\

Also look at this MSDN article for a full guide and explanation.

Note that for more recent versions, you will be looking for the MSBuild standalone package rather than the framework -- see @Vadzim's answer.

Of course. Do:

sudo apt-get install mono-gmcs

Everyone else assumed Windows and MS .NET, but...

Yes, if you have the .NET SDK, it's there. For example,

C:\WINDOWS\Microsoft.NET\Framework\v[your version number]\csc.exe

msbuild.exe should be there too, and you can use that to build project (.csproj) files.

Contrary to what some of the other answerers say, you do NOT need the SDK, just the .NET Framework to get the C# compiler, csc.exe.

Also, consider other (free) IDEs like MonoDevelop, #develop, and Visual C# Express. (You said you don't want Visual Studio, not that you don't want an IDE at all ;) )

Yes, there is even an open source one, IDE SharpDevelop. You can set the compiler as a command in UltraEdit (or some other editor of preference), etc.

Yes, but you need to download and install .NET Framework SDK.

Here's a link that can help you.

You only need the .NET framework. You can use Notepad to edit and the CSC.exe to compile.

Assuming you have Visual Studio installed with C# included. Also, assuming you want latest version.

1. Find the path to your VS installation. Call it VSPath.
2. The CSC Compiler will be at VSPath\MSBuild(MSBuild-Version)\Bin\Roslyn

Like some others have mentioned MSBuild is deployed with the .NET Framework (versions 2.0 and 3.5) so if you have either of those installed you can build your applications without needing Visual Studio installed on the machine.