Until November 2009, Sprint operated a webpage called "IP Relay" that allowed anyone with a web browser to type in a phone number, and have a live operator call that number. The operator would then read whatever you typed into your web browser to the person (or voicemail) on the other end of the line, and relay any responses from the other party back to you. Details from Wikipedia can be found here.

Obviously, one could have the operator call your Google Voice # and one could record the "conversation." Needless to say, a fair number of people had some fun with this service. Some Appealing Industries examples are below.