How to remove the hash from window.location (URL) with JavaScript without page refresh?

Solving this problem is much more within reach nowadays. The HTML5 History API allows us to manipulate the location bar to display any URL within the current domain.

function removeHash () { 
    history.pushState("", document.title, window.location.pathname
                                                       + window.location.search);
}

Working demo: http://jsfiddle.net/AndyE/ycmPt/show/

This works in Chrome 9, Firefox 4, Safari 5, Opera 11.50 and in IE 10. For unsupported browsers, you could always write a gracefully degrading script that makes use of it where available:

function removeHash () { 
    var scrollV, scrollH, loc = window.location;
    if ("pushState" in history)
        history.pushState("", document.title, loc.pathname + loc.search);
    else {
        // Prevent scrolling by storing the page's current scroll offset
        scrollV = document.body.scrollTop;
        scrollH = document.body.scrollLeft;

        loc.hash = "";

        // Restore the scroll offset, should be flicker free
        document.body.scrollTop = scrollV;
        document.body.scrollLeft = scrollH;
    }
}

So you can get rid of the hash symbol, just not in all browsers — yet.

_{Note: if you want to replace the current page in the browser history, use replaceState() instead of pushState().}