jQuery - Add ID instead of Class

I'm using the current jQuery:

$(function() {
    $('span .breadcrumb').each(function(){
        $('#nav').addClass($(this).text());
        $('#container').addClass($(this).text());
        $('.stretch_footer').addClass($(this).text())
        $('#footer').addClass($(this).text());
    });
});

It applies the text held in the breadcrumb to 4 elements on the page, allowing me to style specifically to the page there on.

I'd like to try adding an ID instead of a class, how can I achieve this?

Try this:

$('element').attr('id', 'value');

So it becomes;

$(function() {
    $('span .breadcrumb').each(function(){
        $('#nav').attr('id', $(this).text());
        $('#container').attr('id', $(this).text());
        $('.stretch_footer').attr('id', $(this).text())
        $('#footer').attr('id', $(this).text());
    });
});

So you are changing/overwriting the id of three elements and adding an id to one element. You can modify as per you needs...

Keep in mind this overwrites any ID that the element already has:

 $(".element").attr("id","SomeID");

The reason why addClass exists is because an element can have multiple classes, so you wouldn't want to necessarily overwrite the classes already set. But with most attributes, there is only one value allowed at any given time.