Not every article will have a DOI.  DOI (Digital Object Identifier) or other unique identifiers assigned to articles have only come into widespread usage within the last 10 to 15 years.  Older articles may or may not have a DOI,  The older the article is the less likely it will have a DOI.  The more recent the article the more likely it will have a DOI.  Some databases such as PubMed now include the DOI in the citation to the article. 

Most publication styles and formatting guides, such a AMA or APA, require a DOI be included in a citation or reference to an article if a DOI exists.

You can use this DOI Lookup Tool to find the DOI of most articles:  

http://www.crossref.org/guestquery/