If you are using the scripts of metro UI css (excellent free metro UI set from http://metroui.org.ua/) , that can clash too. In my case, this was the problem recently.
So, removed the scripts reference of metro UI (as I was not using its components), datepicker is showing.
But you cant get metro look for datepicker of jQuery-ui
But in most cases, as others mentioned, its clash with duplicate versions of jQuery-UI javascripts.