A few additions:

Insteadt of a polling mechanism it could be alternative registered an object which will be passed to all event-handlers e.g.

var socket = new WebSocket(...);

socket.onmessage = function(event, myObject)
{
  ...
}

...

or another alternative is a waiting function on the object insteadt of polling. E.g.

var socket = new WebSocket(...);

socket.send(...);
var reply = socket.waitForData();

But in this case only one event handler (onmessage) will be used. After a reply is arrived there must be checked which reply was it.

The second comment with the idea of "myObject" is superfluous. I have found a way to do this now. But the other two my be a thought worth.

There's no way we'll add polling.  Polling in JavaScript is a terrible, terrible idea, because as long as script is running, the page (possibly the whole browser) is frozen.  That's why everything is event-based: JS is on the same thread as layout, and nothing can render as long as JS is running.

If you need access to a specific variable, try nesting your functions.  For instance:

function setUpSocket() {
    var myObj = initializeObject();
    // set up websocket
    s.onmessage = function() {
        // Do processing that includes access to myObj
    }
}

This is awkward sometimes, but it works.

If the WebSocket connections is managed by a Web Worker then no page freeze occur and polling might be possible. 

I have found already the solution like you mentioned with nesting. Thanks.

Nice Weekend.
René

AFAIK, IndexedDB exposes synchronous APIs that are only usable in Web Workers.  That's something that should be doable for WebSocket, and might be a good idea.  We don't want to require polling in that case, though -- just make it block.

It's easy to do this already:

   var queue = [];
   websocket.onmessage = function (event) {
     if (queue.length)
       queue.shift()(event);
   };

   // to send and then wait for response:
   websocket.send('foo');
   queue.push(function (event) {
     // rest of function goes here
   });

...or some such. Basically works like polling but without having to worry about missing other events if you have other things going on.

(code above is untested so may have syntax errors)