<p>Is the edit control I'm typing in now, with all its buttons and rules freely available for use? </p>

<p>My web project is also .Net based.</p>

It's the
WMD
Markdown editor which is free and seems to be pretty easy to use.  Just include the javascript for it and (in the easiest case), it just attaches to the first textarea it finds.
Here's some info about the
Perl implementation of Markdown
which, according to the site, WMD is 100% compatible with.
@Chris Upchurch
Technically the current release isn't open-source, just free to use.  The next version is supposed to be released with an MIT license though.
"now completely free to use. The next release will be open source under an MIT-style license."