Bo - I cut down towels to make wash clothes. I split worn sheets down the middle and sewed the sides together to make the center seam and hemmed the edges. You could make a "double" bed sheet that was wearing thin work very nicely for a long time on a single bed by doing this.
Granny G - I still cut sheets down the middle and sew the outer edges together. Also join the best parts of towels to make bath mats. Only in the last few years I have stopped darning socks, as I just don't have time. I unpicked a jumper of mine, and used the wool to knit a dressing gown which passed along to each of my four children. I used to make the children's clothes, but when they get to a certain age, they want the brands that all the other kids are wearing.