System.IO.IOException: The handshake failed due to an unexpected > packet format?

It looks like a problem with SSL authentication, it fails at handshake phase, maybe two implementations are not compatible, you may check the WSDL format of the response, figure out what format should be used for communication and check if the one sent by you complies with it (you may use any kind of a network monitor software, eg. Microsoft Network Monitor)

I just wanted to make an answer based on one of the comments because it can cause this error to happen.

In some cases, if you have a BaseURL while calling a API, then the problem could happen if you mixed up http and https. This happened in my case while calling a Google API. This is a simple fix in some cases and can happen to anyone.

Hope this help's someone out.

In my case it was Skype blocking 443 port. Go to Skype tools-advanced-connections and disable "Use port 80 & 443 for connections..."