Maybe the most obvious, use them as dust cloths. The diapers are super soft and lint free so buff away dust and they won't damage surfaces.
Replace disposable dust cloths on static sweepers. Just attach them the same way you would with the disposable kind, just toss them in the wash when you're done.
Cut strips of diapers and use as a buffing cloth for polishing shoes.
Use diapers to wrap small fragile items before you store them away.
You can also use cloth diapers as tack cloths when you're sanding or to spread and remove stain on woodworking projects.
Use to protect edges of wood or furniture that you're transporting to protect it from scratches or dents from bungee cords.
Who knew such a utilitarian item could be so handy around the house? I'm Mrs. Fixit and it's just that simple!