I learned about composting old clothes while watching a very funny and odd "instructisode" by The Guide Girls. They're a comedic/environmental duo who make informative videos about greening your lifestyle. My friend Sarah told me about them, and I recommend that you check them out. They're funny and helpful.
Anyway, I decided to try putting some old socks in my compost pile. I chopped them up into small bits to help them break down more easily, and I cut out the elastic band at the top. Dakota goes through a lot of socks, and we can't use all of them as rags. So, this seems like a great way to get rid of old cotton clothes that can't be donated, like socks, underwear and, well, rags.
Speaking of composting, a couple of friends recently asked me what kind of kitchen compost bin I'd recommend. I've tried a few options, including the plastic kind with the charcoal filter in the lid, and I think my current setup is my favorite. It's a stainless steel pail, which doesn't absorb any gross smells or harbor any nasty bugs. For easier dumping and cleaning, we line the bin with BioBag Waste Bags, which break down in the compost bin. Basically we just dump it, spray it down with the hose, let it dry in the sun and it's ready to be refilled with kitchen scraps.
I know other people like to keep their compost in a resealable plastic container in the freezer. That seems like it would work pretty well, too.