As you migth know, is quite usual that when you publish and article in a journal you transfer the copyright of the article to the journal for a particular period of time. Therefore, each journal would stablish this particular time, in which one you should´t re-publish the complete article in your website (you can give the reference of it). Once this period is gone, your are free to disseminate your article as you want.
You can freely use the papers published in open-access online periodicals. For others you will have to follow the copyright rules as pointed out by Maria.