By default, browsers don't allow cross-site AJAX requests.
I understand that a badly envisioned cross-domain request can be a security risk. If I take the html or the javascript of an external site and just "render" it into my website, that's a problem. That external code could be used for lots of bad things - like getting access to the current user's session data.
But if I only request JSON or XML data, and I use a proper library to parse the JSON (not just using eval) I can't imagine how that would be a security risk. The worse that can happen is that the content coming from that site doesn't render correctly.
Am I missing anything? Is it possible to compromise a page that reads json/xml simply by sending it some kind of malicious data?