i dye them, with Fiber Reactive Procion Dyes, and soda ash for a fixative for cotton, then i tear them into strips and make crochet rugs, i just buy the primary colors and tub dye, so sometimes they are beautiful, sometimes ugly, but at least i have something to do with them. (providing they have not been stolen for rags, lol)

I use mine to cover our porch furniture during the winter months

drop clothes for when you paint.
Mom used some in the garden if she heard of an early frost possibility to cover plants to protect them.

If you sew clothes, or wand to try out a pattern for domensions, fitting,etc. use the old sheets for your trial. If you like it, you then have a fabric pattern to go by.
I did this with dresses I fitted bridesmaids for. I used old sheets for the fitting "dress". Used them up and didn't add any cost to the bridesmaid.
I have also used the sheets for pillow stuffings. I make a pillow out of the sheets and stuff it, then place that in the pretty pillows that I have created. This makes the outer case washable/cleanable easier.

Some terrific ideas, thank you all!