PROBLEM: Though they are made largely of paper, most single-use cups are lined with a fine film of polyethylene. This lining makes the cups liquid proof but also difficult and expensive to reprocess (because the materials have to be separated). As a result, these cups cannot be recycled at standard material recovery facilities.
SOLUTION: Avoid disposable coffee cups all together by carrying your own mug or travel cup. Only buy coffee on the go when you have a reusable cup to carry it in.