OK, I think I have a new favorite thing to knit for kids.
Could this be any cleverer? It's a ball made out of six (or you can do nine) plain knit bands, woven together in what's really a cube, but which turns ball-like with a little squishing.
You knit six bands of stockinette stitch, and the pattern takes advantage of the fact that stockinette curls in on itself. That turns what would be long flat panels into narrower plump bands.
For this one, I used leftovers from: baby sophisticate, from the dyed yarn for the ten stitch twist blanket, and a pair of golden monkey socks (that yarn was used doubled). I had to cut the bands down in length from the original pattern (which I can only find a link to from ravelry) to make the ball firm enough--originally it was a little too loose, which I fortunately realized when I had only four of the bands woven together and was knitting the fifth. The shorter bands make it harder to weave the last band, in particular, but give it much better shape.
Basically? Highly recommended. I'm going to make another this size out of more leftovers, and then possible a couple out of sock yarn alone (those will obviously be smaller) to use as cat toys.