Depends which country you are in - UK libraries don't usually have access to academic journals.
How about local university libraries then?
They are generally not open to the public, and when they are you are rarely allowed to access electronic journals because of the licence agreement which the university has signed with the publisher.
Same in the US.
Really? Perhaps the British Library, yes, but not my local. Not even my university has access to most journals. Thankfully I have two separate accounts at different universities so I can usually find what I'm looking for.
At my local library (largest in my state) you have to be on one of the library computers to access any pay journals. Which is annoying, especially since I would have to wait for a spot.
Do most local libraries in the US really have unrestricted JSTOR access? Here only the University libraries have JSTOR and they only make it available to students and faculty.