When I was last in the states, I found some wonderful all cotton sheets at a thrift store for $1.50 each. They were very high quality sheets and not at all "worn out" and wonderfully white--very, very white--and not thin at all. I've been using them in some of my charity quilts and I love them. Plus, I found about 6 or 7 of them --all the same, so that meant I had a lot of that fabric. (They weren't the kind that is so tightly woven that you can't quilt them, either. I've experienced that as well! That is something else to watch for.)
Just be picky about what you choose--you can find good stuff that is sent to the thrift stores. A lot depends on where they get the donations.