This is useful as a basis:
How to programmatically connect a client to a WCF service?
However, I’d like my client to do the same thing REST-style without knowledge of any service contract.
Seeing how this is done easily in Javascript / jQuery, it seems odd that C# presents no options.
In C# all you need is a standard HttpWebRequest or WebClient like this:
or
Of course you still need to do something with the XML or JSON (or whatever data format is returned) but that is no different in JavaScript with jQuery.