I used to go the the library and read the magazines I really like which are:
1) Rolling Stone
2) The Utne Reader
4) The Atlantic
5) The Sun (a local literary magazine out of Chapel Hill, North Carolina)
7)The Paper Soldier (this is the literary magazine produced by the prison where I work).
8) The New Yorker and Vanity Fair (depending on what articles are included that particular month-I find them to be inconsistent in their content these days - I used to love the New Yorker unreservedly - but it's not the same quality it used to be).
When I lived in the United States, in Maine, New York and North Carolina we were allowed to check out the back issues of magazines. I always did that. Over here you can't do that, so I don't read them nearly as much as I used to- any of them.
I do read the Times Literary Supplement sometimes.
I also go to the library to read the newspaper during my lunch break as I work at an educational facility which actually has a very fine library. I buy a newspaper on Saturday and Sunday - I buy the Saturday Guardian and the Sunday Times.
I am very careful about paper usage and wastage. It's not so much the economy as the fact that I feel it's more reasonable to read them in the library.
I don't read very much online at all. I like holding reading material in my hands.