I know this thread is a bit dated and some of my ideas might be repetitions of ideas mentioned above, but they might still be a bit more detailed.
If only the toe part is beyond repair, fingerless gloves are a great idea. To make them a bit more special you could also add a bit of lace for the fringe and/or some sort of ornament (e.g. a crocheted flower, a beautiful button, whatever ...).
Puppets are, of course, the obvious idea and great if you have kids.
If the heels are gone, wristwarmers are a better idea. You dont need a hole for the thumb and can just wear them like bracelets. Or even together with bracelets. Or you might consider decorating them with beads, ornaments or lace so you don't need any other bracelets.
The parts that you have to cut off can easily be used as stuffing for other projects.
If you don't like wristwarmers, you can still make your socks into little wallets, bags, mobile phone covers or purses. All you have to do is sow one end and put a zipper, button or velcro on the other end. If you want to, you can also put either the other sock or some sort of cloth on the inside.