You can't really "launch an application" in the true sense. You can as you indicated ask the user to open a document (ie a PDF) and windows will attempt to use the default app for that file type. Many applications have a way to do this.
For example you can save RDP connections as a .rdp file. Putting a link on your site to something like this should allow the user to launch right into an RDP session:
<a href="MyServer1.rdp">Server 1</a>