How do I get the n-th level parent of an element in jQuery?

Depends on your needs, if you know what parent your looking for you can use the .parents() selector.

E.G: http://jsfiddle.net/HenryGarle/Kyp5g/2/

<div id="One">
    <div id="Two">
        <div id="Three">
            <div id="Four">

            </div>
        </div>
    </div>
</div>


var top = $("#Four").parents("#One");

alert($(top).html());

Example using index:

//First parent - 2 levels up from #Four
// I.e Selects div#One
var topTwo = $("#Four").parents().eq(2);

alert($(topTwo ).html());

You could give the target parent an id or class (e.g. myParent) and reference is with $('#element').parents(".myParent")

Since parents() returns the ancestor elements ordered from the closest to the outer ones, you can chain it into eq():

$('#element').parents().eq(0);  // "Father".
$('#element').parents().eq(2);  // "Great-grandfather".