Teaching Citation: Are there any Journals which Fully Apply APA, MLA or Chicago Citation Rules I'm interested in doing a little casual survey.  As many of us have been through undergraduate training where citation rules are expected to be applied exactly, and sometimes even marked as if they were mathematical equations, I'm wondering if all that learning is even worth it.  Does anybody know of any major or middle-level journals which actually demand any of the major citation systems to be applied, or do all such journals have in-house systems?

If most journals do demand strict adherence to any of the style manuals then it follows that there is good reason to teach such systems, but if none or few do, then these systems should not be taught as they are but adapted to what is actually practiced.
I believe all the journals published by the APA request strict adherence to the APA style manual. Similiary, PMLA, one of the two journals published by the MLA, asks for submissions in MLA style. University of Chicago Press publishes a lot of journals, but the first one I found asks for submissions in Chicago Style.

My experience with APA journals is that they allow for fair amount of flexibility in the submission format. I doubt any journal will reject submissions that use italics instead of bold or a comma instead of a period. They will likely fix these issues during copy editing,

As for the comments on the questions that just use Endnote or BibTeX/Biblatex to handle it, the problem is that most of these style guides are not designed to be programmatically implemented. It took a lot of work to get biblatex to fully implement APA 6 and there is no BibTeX version that is fully compatible.