Get selected value of a dropdown’s item using jQuery

How can I get the selected value of a dropdown box using jQuery?
I tried using

var value = $('#dropDownId').val();

and

var value = $('select#dropDownId option:selected').val();

but both return an empty string.

For single select dom elements, to get the currently selected value:

$('#dropDownId').val();

To get the currently selected text:

$('#dropDownId :selected').text();