Dowsabella, we must be of the same generation. Mum and dad kept said bits of string, brown paper etc. I was usually give the job of undoing the knots in the string. Mind you, dad was a jolly good 'maker and mender'. When he was alive, neighbours would ask if he could use various bits of wood, and he would squirrel them away, often to be used for some project or another.
As a moving in present, to our new house, when we married, mum gave me a small paper package containing a piece of coal, so that we need never be cold. I still have it in a kitchen drawer.
I used to keep boxes that things like TV's and mixers came in, just in case, but recently have cleared out a lot from the loft, and I am also getting better at clearing clothes from the wardrobe, that I haven't worn for a long time.
DH has at least two drawers of bits of 'electrical string' with various plugs attached. We don't need any of them, but he won't get rid.
Why have we got half full/ empty tins of paint in the garage?
I guess it is the wartime habit of making sure you don't run short.