I agree your mind doesn't stop, but sometimes I solve my problems in that moment before sleep, I think because I can direct all my energy to it (even eyes are closed, so no visual processing needed).
Though the tired mind is often very keen to simply recurse over thoughts you've already had opposed to think of new ones. If you find you can't stop yourself going over the day though, then 10-15 mins of meditation, where you force yourself to concentrate on clearing your mind, can stop these thoughts so you can sleep. Do this every night for a few weeks and it becomes second nature.
I've found that reading sci-fi/fantasy before going to sleep helps me transition to sleep mode. I think it's because sci-fi problems are really somebody else's problem, so my brain can let them drop when I put the book down.
I really couldn't agree with this more. Reading before you sleep is so important to getting a good night's rest. Using a physical book or an e-ink screen, anything that doesn't emit light itself.
Seriously, invest $150 into getting a good e-reader, if you don't have one already. It's well worth the sleep benefits, potentially even more than a good mattress (for a programmer, anyway).
One thing I personally found useful was f.lux - an OS X app that changes the temperature of your screen when it gets dark outside. Sounds trivial but makes a huge difference.
Though the tired mind is often very keen to simply recurse over thoughts you've already had opposed to think of new ones. If you find you can't stop yourself going over the day though, then 10-15 mins of meditation, where you force yourself to concentrate on clearing your mind, can stop these thoughts so you can sleep. Do this every night for a few weeks and it becomes second nature.