Some nice ideas thank you!Hopefully, 100% cotton sheets.
One of my favorite use has been cutting and sewing them into pillowcase-like bags to put strings of Christmas lights into - one strand per bag. Very little additional wear to the fabric, very quick and easy to put the lights away, same for getting them out, adds some cushioning so the bulbs aren't scratched or banged, the wire doesn't tangle or kink.
I made similar bags for the lionel train cars. Also folded pieces of worn out sheet accordion style with a piece of track in each fold. This has all the advantages that the bags had for Christmas lights. It is lighter weight, less bulky, and more consistent than any of the several other methods I tried.
Sleeves for dishes if you have any in storage. I have a small set kept up in the kitchen and enough extra kept in the basement that I bring up when more than come. And some keepsake dishes that I don't have a place to display right now. My sister in law did a level better. She had the same dishes as her next door neighbor. They borrowed dishes from each other when either had a lot of company.
Patches for clothes, quilt batting, flags for the tops of stakes or tree branches for landscaping or gardening, dust covers (such as for stored furniture, out of season lawn equipment), drop sheets to catch saw dust or whatever, tablecloths (not usually good for aesthetics but good for under crafts or to protect a table from scratches when sorting dirty things or such), handkerchiefs.
repurposing signs: I made an envelope out of a plain colored sheet that slid down over the top of the sign the roofers left at the end of the yard. On the envelop, I made thick, black letters "SALE" when I had a yard sale. It worked much better than the poster board versions. It also hargs neatly on nails on the garage wall behind some of the shelves.
Dolls or doll clothes.
Rag carpets - cut into strips and braided, hooked, or sewn to a backing. This os the only one of these I haven't done myself. I have some other people made from similar fabric.
Ripped up strips make good tinder.
Scarecrows body or clothes. Flags tied to fence wire to show animals where the fence is.
In all cases, not every sheet is necessarily good for every use. Since most of the wear is on the middle of the sheet, sometimes the outside edge is better for a given thing. Sometimes the threadbare middle is.
Edit to fix typos
There are some fabric collection places but not nearly as common as in Europe.