Javascript in browser IS able to use sockets/get info from web by itself?

Is it possible to open sockets and get data from web in JavaScript.

My aim is: to work with web data using JS. I have looked for XmlHttp/AJAX solution, but I have found one note, that AJAX can be used only for calling localhost programs, which will be used as proxy and then only returns data from web.

It's because of sandbox model in browsers, which don't allow to work with sockets/other sites from JavaScript, and it works only in localhost.

Are there any solutions with JS to work with other world?

Your issue is due to cross domain request security, where you can't asynchronously get data from a domain which doesn't match the current host (this includes subdomains). You can however use jsonp, but this relies on the service that you're quering to supply the data in a jsonp format (a function call with the json data as a response).

If you have no control over the services you're requesting (which i assume you don't), you can use a javascript library, such as YUI or jQuery to perform the cross domain request for you (which typically uses Flash as the data proxy). However this will only work if you the site in question allows cross domain requests from your domain (defined in crossdomain.xml).