Here's something I'm adding to my To-Do list - a fabric basket.
I found this at Sew4Home. This one was made for a baby nursery. The link includes a complete tutorial! It's just fabric with recycled cardboard reinforcements. It's made in a way that allows it to be completely collapsed for easy storage. My goodness. That makes it even more versatile!
This could be made with all sorts of different fabrics. The tutorial includes instructions for altering the size.
Think of all the places you could use this - in the closet, in a craft room, in the car ... well, I could go on for ages.