Before the internet, research papers in the actual paper form were kept in the libraries of universities. I have spent many an hour looking at them in such libraries. At a newly built university, UC Merced, I recently discovered that there are no holdings of scholarly journals in the physical form (which was so nice, because you could look at them without belonging to an institution or paying $40 per paper as you have to online).
However, I think generally the older universities will not have thrown away their massive collections of journals in the paper form, and one should still be able to find them in their libraries.