Borrow - I'm a HUGE fan of my public library. And by being such a regular borrower, I'm helping my own little library out because the more their books circulate, the better off they are. I feel like borrowing from the library is part of my civic duty.
That said, I buy books that I love. So I guess I do both.
Also? I don't really care about library fines - if I need to keep a book longer, I just keep it and pay my fine when it gets up to $10.00. Just another way of supporting my public library.