I am sort of addicted to making foundation-pieced crazy quilts, so I keep my eyes open for really thin fabrics at yardsales and thrift shops to use as my foundation; or super sales on really thin muslin. For that purpose, thinner is better, to a certain limit.
Cheap fabric can be used to test patterns a lot of the time. I'm STILL hunting for the "perfect" teddy bear pattern and have made a few mock-ups out of some awful fabrics I had on hand. For that I just have to make sure it's not unusually stretchy, since I'm trying to get a good idea of the bear's shape. The dogs get my test bears as toys, they don't care what the fabric looks like!