What I did to continue having access to articles, even tho I am no longer affiliated with my alma mater, was to apply for an alumnus ID (lifetime membership in my case!) that allows me to make at most three free(!) trips to the university library a month. I then keep a running list of articles I want to read as I encounter them (e.g. on MO or anywhere else on the Internet), and then take this list whenever I go paper-chasing in the university library. In there, they allow you to print online journals or photocopy paper journals for a very nominal fee. (It also helped in my case that I was good friends with the librarians even before I graduated.)
I've figured at this point that the price I paid for my alumnus ID, altho relatively a rather substantial sum, is way much less than the sum of the cost of all the articles I have, if I had directly paid the publishers for them.
You might want to look for a similar deal in your libraries.