The greatest example I can think of is the Google Chrome installation.
I remember one other application launching that same way. Can't remember what it was. I'm not implying that it was built in C# or even .Net.
It is possible somehow. It's been done. Just wondering how.
I think what you are asking for is ClickOnce deployment.
ClickOnce deployment allows you to publish Windows-based applications to a Web server or network file share for simplified installation
Are you talking about launching an application or installing it? You can launch an application by registering your application has a protocol handler (such as http://) within Windows...different browsers will have different behaviors, but it's possible that way. See this link for information.
Someone else has already pointed out ClickOnce, and this is probably want you want. Another alternative is Silverlight, where the application runs inside the browser window.