APA prefers that you use a DOI rather than a URL, but if you are using an online source and there is no DOI, you should include a URL.
The purpose of providing a URL is to allow someone else to locate your source. Since specific URLs often change, it is usually best to link to the homepage of whatever journal or organization is responsible for the content you are citing.
So, let's say that you find the following article in the database Academic Search Premier:
Trepal, H. C. & Wester, K. L. (2007). Self-injurious behaviors, diagnoses, and treatment methods: What mental health professionals are reporting? Journal of Mental Health Counseling 29(4), 363-375.
Academic Search Premier provides the following "Permalink" for this document:
This link is a) ugly and b) of no use to those without access to EBSCO databases such as Academic Search Premier.
So, the appropriate URL to use would be the homepage for the Journal of Mental Health Counseling:
Generally, you can find journal homepages with a simple Google search.
The entry in your reference list would look like:
Trepal, H. C. & Wester, K. L. (2007). Self-injurious behaviors, diagnoses, and treatment methods: What mental health professionals are reporting? Journal of Mental Health Counseling. 29(4), 363-375. Retrieved from http://www.amhca.org/news/journal.aspx
There are situations in which providing a more complete URL may be useful. One example would be a document on a publicly available website that is difficult to search.