You can make cross domain requests using the XMLHttpRequest object. This is done using something called "Cross Origin Resource Sharing". See: http://en.wikipedia.org/wiki/Cross-origin_resource_sharing
XMLHttpRequest
Very simply put, when the request is made to the server the server can respond with a Access-Control-Allow-Origin header which will either allow or deny the request. The browser needs to check this header and if it is allowed then it will continue with the request process. If not the browser will cancel the request.
Access-Control-Allow-Origin
You can find some more information and a working example here: http://www.leggetter.co.uk/2010/03/12/making-cross-domain-javascript-requests-using-xmlhttprequest-or-xdomainrequest.html
JSONP is an alternative solution, but you could argue it's a bit of a hack.
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