Many of the articles on this website would not have been possible without access to sholarly, peer reviewed journals. Being a university student makes journal access 1,000 times easier, as there are hundreds of walls set in place for sholarly journal access due to large bloodsucking publishing companies whom universities and colleges pay millions of dollars to a year. Open access can't come soon enough! In a year I'll be out on my ass, and my fortunate opportunity will have passed on by. I have compiled a short list of alternative ways to access scholarly journals without necessarily being a college student. Please comment if this proves helpful to you in any way, or if you know of an alternative method.
/r/scholar - is probably the easiest way to access whatever you're looking for. It is a community of redditors who have journal access, and will find for you whatever journal article you need. If you currently have journal access, consider "paying in" to the system with the hope that others will do it for you in the future. If you are going to post there, read the guidelines on the right of the page.
Get in touch with your nearest university library - My host institution has gratuitous requirements for obtaining a library card. This will grant you journal access in the library, and perhaps e-journal access. It may sometimes be possible to get journal access just by using the library's Internet to access the databases. This probably works best with public institutions.
Get in touch with your former university or college - Nazareth College was willing to set me up with my old .edu email address even though I transferred four years ago. Many schools will not let you keep your student email after graduation. I found that I was also able to use my library account. Although this may have been a fluke, it's worth the phone call.
Directory of Open Access Journals - requires no membership or fees.
Your local library - has a list of databases you can access with a library card there, once again just a phone call away. They may get you copies of journal articles through inter-library loan if you cannot access the digital version of the article.
Google Scholar - Provides a search of scholarly literature, although is very limited in that it may only pull up certain pages of the journal article you are trying to read.
arxiv - is Cornell's open access archive of physics, mathematics, computer science, Biology, Finance and Statistics journal articles.