This weekend, I mentioned getting creative. It's hard to do that (efficiently, anyway) if you're not organized, though, at least a bit. So, after spending over half an hour untangling my bobbins (I wish I had a before picture), I decided I'd better prevent this from happening again, and came up with what you see above. The box was the packaging for an old necklace (I think an Altoid tin might stand in here nicely). I cut strips from a a cardstock piece of junk mail for the partitions; it was a good movie-time activity.
The only thing I think I'd change is to make the partitions only half the height of the bobbins, so I could pick them up more easily. All in all, though, I'd call it a success, and free at that!