This is just one idea, I'm sure there are hundreds more out there, but as there have been a few birthdays I've been putting together "build a fort" kits - very simply you take an unwanted but unripped sheet, cut strips from an old tee shirt and make loops and ties at each corner and down the sides/ smack bang in the middle of the sheet. (sew these on) visit your local $2 store and pick up some pegs, rope and a torch and bob's your father's brother, one self build fort.
There are several blogs out there which already show you how to do it, so I won't reinvent the wheel, but send you to have a look instead.
Salt Water Kids
But anyway, here's one of my version - I forgot to get photos of the other so you'll just have to imagine.
So, what can you use an old sheet for?