Is it legal for a university to post a copy of a copyrighted (pay for access) journal article? Extensively using Google Scholar, I've realized that most of the articles belonging to  publishers that limit access to material (i.e. ACM, IEEE, Elsevier) also have PDF versions available for free, and these files usually are hosted by universities or other aggregators like ResearchGate.

Is it legal for the university/organization to host a copy of an article, if this has been published on a conference or journal with paid access? Does it matter if the authors of the article belong to that university/organization?
To answer the (original version of the) question in the title:


  Are scientific articles of public domain?


the answer is absolutely not, unless the relevant copyright holders declared it so or that its copyright has expired. Note that public domain is emphatically different from open access. 

To answer the question in the body:


  Is it legal for the university/organization to host a copy of an article, if this has been published on a conference or journal with paid access? Does it matter if the authors of the article belong to that university/organization?


the answer is it depends. 

What does it depend on? Very simply, the publication agreement or the copyright transfer agreement or the licensing agreement signed by the author when the article has been accepted for publishing. For example:


Here's the version for Science
Here's the one for IEEE
Elsevier compiled a handy table for their journals. 


As David Ketcheson points out below, a great resource for checking the self-archiving and open access policies of is Sherpa/Romeo.