I have a slightly modified JSFiddle to support my production JQuery version (1.10.1, original version uses 1.4.3). I could not get 'Remove' link to remove newly created <p>
after I click on 'Add new input box'.
I think the problem is located in
$(this).parents('p').remove();
Modified version: http://jsfiddle.net/x68jx/
Original version: http://jsfiddle.net/jaredwilli/tZPg4/4/
For dynamic added element, you have to use event delegation. And id should be unique, so use class instead.
The WORKING DEMO.