The Digital Object Identifier (DOI) was created to be an easier, more permanent way to track down a source in a citation list. However, its newness, lack of universal inclusion, and way of being buried on a journal's web page can make including this a source of frustration.
The APA Manual does not require that you include a DOI--it only recommends that you include when when it is available. Make the best effort possible to track down the DOI. See pages 187-9 in the APA citation manual.
Here are a few of the main aspects that characterize APA style: