Griff is right, but I want to add two cents:
The better question is: "can I run the C# application without Windows?" The answer is "Yes, in many cases".
Are you sure you understand the role of .NET? As Window was historically a framework and run-time host on top of DOS, now it gradually happens to .NET. I really hope that Windows will die, but .NET will not. Even now I know several developing platforms based on pure .NET (more exactly, ECMA/ISO CLR specifications).
.NET is available on many OS in the form of standard-compliant Mono software (
http://en.wikipedia.org/wiki/Mono_(software)[
^]). I run my applications compiled on Windows (even with Forms) on my Linux machine without recompilation.
Practically, it's good not to afraid about having .NET installation, it becomes a common place and is bundled with newer versions of Windows. Even if it is not, the comprehensive solution is to deploy .NET re-distributable with the installation of application, which is not so hard to do.
Start from this:
http://msdn.microsoft.com/en-us/library/6hbb4k3e.aspx[
^], see also:
http://www.netomatix.com/articles/KBArticle.aspx?a=324733[
^].
Google:
http://en.lmgtfy.com/?q=(deploy+OR+deployment+OR+distribute+OR+distributing)+.net+framework+with+application[
^].
—SA