If the server sends some status code different than 200, the error callback is executed:

$.ajax({
    url: '/foo',
    success: function(result) {
        alert('yeap');
    },
    error: function(XMLHttpRequest, textStatus, errorThrown) {
        alert('oops, something bad happened');
    }
});

and to register a global error handler you could use the $.ajaxSetup() method:

$.ajaxSetup({
    error: function(XMLHttpRequest, textStatus, errorThrown) {
        alert('oops, something bad happened');
    }
});

Another way is to use JSON. So you could write a custom action filter on the server which catches exception and transforms them into JSON response:

public class MyErrorHandlerAttribute : FilterAttribute, IExceptionFilter
{
    public void OnException(ExceptionContext filterContext)
    {
        filterContext.ExceptionHandled = true;
        filterContext.Result = new JsonResult
        {
            Data = new { success = false, error = filterContext.Exception.ToString() },
            JsonRequestBehavior = JsonRequestBehavior.AllowGet
        };
    }
}

and then decorate your controller action with this attribute:

[MyErrorHandler]
public ActionResult Foo(string id)
{
    if (string.IsNullOrEmpty(id))
    {
        throw new Exception("oh no");
    }
    return Json(new { success = true });
}

and finally invoke it:

$.getJSON('/home/foo', { id: null }, function (result) {
    if (!result.success) {
        alert(result.error);
    } else {
        // handle the success
    }
});

After googling I write a simple Exception handing based on MVC Action Filter:

public class HandleExceptionAttribute : HandleErrorAttribute
{
    public override void OnException(ExceptionContext filterContext)
    {
        if (filterContext.HttpContext.Request.IsAjaxRequest() && filterContext.Exception != null)
        {
            filterContext.HttpContext.Response.StatusCode = (int)HttpStatusCode.InternalServerError;
            filterContext.Result = new JsonResult
            {
                JsonRequestBehavior = JsonRequestBehavior.AllowGet,
                Data = new
                {
                    filterContext.Exception.Message,
                    filterContext.Exception.StackTrace
                }
            };
            filterContext.ExceptionHandled = true;
        }
        else
        {
            base.OnException(filterContext);
        }
    }
}

and write in global.ascx:

 public static void RegisterGlobalFilters(GlobalFilterCollection filters)
 {
      filters.Add(new HandleExceptionAttribute());
 }

and then write this script on the layout or Master page:

<script type="text/javascript">
      $(document).ajaxError(function (e, jqxhr, settings, exception) {
                       e.stopPropagation();
                       if (jqxhr != null)
                           alert(jqxhr.responseText);
                     });
</script>

Finally you should turn on custom error. and then enjoy it :)

Unfortunately, neither of answers are good for me. Surprisingly the solution is much simpler. Return from controller:

return new HttpStatusCodeResult(HttpStatusCode.BadRequest, e.Response.ReasonPhrase);

And handle it as standard HTTP error on client as you like.