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
    }
});