To solve this, you have one of two choices: either follow the CORS standard supported by the good guys of the browsers (guess what – the usual suspects of browsers don’t support it), or use a proxy within your Web application which is able to dispatch requests to resouces of other domains.
For the CORS approach, there is already a nice blog from Joanna Chan here in SCN. CORS is a good choice if you don’t need to support older browsers, like IE version 8 or 9, and if you are able to securely control the allowed originating domains in your server application or service.
Check out the sources and further documentation directly on github. As we follow an open-source approach here, you are also welcome to propose changes or extensions in case you spot areas in the proxy which shall be improved.