What is a DOI? A DOI (digital object identifier) is a unique alphanumeric string assigned by a registration agency (the International DOI Foundation) to identify content and provide a persistent link to its location on the internet.
NOTE: It is regarded as the most important part of the citation because it will accurately direct users to the specific article.
Think of it as a "digital fingerprint" or an article's DNA!
FYI - Updated rules on using DOI (March 2017):
(Above information from The APA blog on DOI. This is APA's official blog and their staff provides excellent examples on APA formatting/citations.)
If a journal article has a Digital Object Identifier (DOI) listed, you will always include this identifier in your reference. You will not have to include the URL of the journal's home page or of the database from which you retrieved the article if a DOI is available
If you viewed a journal article in an online database and it does not have a DOI, you will need to do a quick search outside of the database to locate the URL for the journal's home page (pp. 191-192). This information must be included in the reference. If the journal is no longer being published and it does not have a home page, then include the URL for the home page of the database from which you retrieved the article (p. 192).
If you viewed a journal article in its print format, be sure to check if it has a DOI listed. If it does not, your reference to the article would end after you provide the page range of the article.