As long as they're cotton, go for it!!
I just used up an old fitted king-sized sheet in some diaper-making. Well, actually I still have some left -- those are HUGE sheets!! So far I've just made pocket-stuffers and internal soaker pads out of the sheeting but they could be used in any part. It will take quite a few layers usually because sheets are often made out of quite thin material, but that's the only alteration of sorts. I

looking around the house to see what I can recycle to use in diapers! I mean, I still love ordering and buying other material, but I love knowing that I'm doing the planet well in a doubly good way by recycling material and then reusing cloth diapers!