Can a non .NET site - .htm/.js - call a .NET WCF or .asmx service via an Ajax GET to return data? Examples?
Yes, but you have to wrap it up in jsonp to support crossdomain scripting. I use jquery to consume REST-like API written in WCF (I say REST-like because making it jsonp violates a lot of REST fundamentals, which I don't care much).
I didn't read it, but Google brought up Consuming Cross-Domain WCF REST Services with jQuery using JSONP.
If you have the ability to modify the webservice as Eugene mentions into a REST service with JSONP, then it feasible. Otherwise, if the webservice is external to you, it is not possible to do so solely from Javascript, as you will need some server side component to send posts.
Even calling .NET WCF webservices from non-.NET languages server-side can be very difficult depending on the complexity of the objects used in the method calls. From having spent a fair amount of time working with callers in Ruby, any amount of complexity in the objects sent to the methods will force Ruby programmers to drop to writing hand XML.