I don't know about where you live, but where I live members of the general public get a year's membership at the local university library for 40 euros. That gives you access to electronic copies of uncounted journal articles as well as the right to check out hundreds of thousands of books (but only fifty at a time).
If neither the university library nor the www work for you, you can always send the first author of the paper a mail and ask whether they might send you a pdf copy. I have done this about ten times (from a private address) and always received a friendly answer with the paper attached, usually within 24 hours. This includes one prompt answer from a bigwig, who didn't forget to thank me for my interest in his work. Another guy sent me paper copies of older articles of his all the way from Florida.
When you think about it, this ain't all that surprising. The typical research paper is read by, I don't know, perhaps fifty people. No wonder authors are eager to move their work under another set of interested eyes.
Some people might still hesitate to use this tactic because they subscribe to the view (probably more common in the German- than the English-speaking world) that professors are somehow an elevated variant of homo sapiens sapiens. The house I grew up in featured a professor - my father - and I can assure you they're regular human beings who sometimes drink too much and fart in their sleep. You have this on authority.