<p>I have a support environment where we connect to many of our customers' systems using VPN and Remote Desktop. Right now, support personnel have to manually set up the VPN connection on their workstation. Is there a way to programmatically create the VPN connection?</p>

Look up the RAS API (Remote Access Service), it's a win32 dll, but you can call it from C#. Here are some links that may help you get started:
http://msdn.microsoft.com/en-us/library/aa446741(VS.85).aspx
http://social.msdn.microsoft.com/forums/en-US/netfxnetcom/thread/28125f40-9c3b-4e77-9bfb-8a975e9b3457/