For physics, mathematics, computer science, quantitative biology, quantitative finance and statistics, there is arXiv, the pre-print service:
http://arxiv.org/ When a paper I want is behind a pay wall, I look for it on arXiv. I don't always find it, especially if the paper is from someone not in the US, but it's an incredibly rich resource.
Some astronomy journals open up their articles after a year, A&A, for example.
There's a "troubling trend," as someone else put it, with predatory open-access journals; see here:
http://www.nature.com/news/predatory-pu ... ss-1.11385
The author of that article maintains a (valuable!) blog with a list of questionable journals:
http://scholarlyoa.com/individual-journals/
I know of one researcher's papers which have been plagiarized in various "journals" repeatedly by numerous others, as in, multiple people using the
same articles and claiming the research, done by the researcher I know, as their own. And the "journals" which have published these plagiarized papers don't care at all, so long as they get their money from the plagiarists.