How to check if the element is not the first-child?

For all li's in #thing that aren't first child:

$('#thing li:not(:first-child)')

see http://api.jquery.com/not-selector/

You can do this just to test an element if it's the first child: $(this).is(':first-child'). Other selectors like :last-child would work too.

You could simply ask for its .index() position (relative to its siblings).

$(this).index();   // returns a zero based index position

If you would like to select everything except the first child, this is how to do it:

$('#some-parent').children().not(':first')