I keep a handy, multi-use cleaning tool in my dish drainer -- an old toothbrush! It has come in handy for cleaning those hard to reach places that I can't get as clean as I would like with a rag or scrub brush (like behind the faucet, or in the ridges of the fridge's water dispenser tray), and it's easy to clean when I'm done using it. Sometimes soap and hot water is all it needs, but sometimes it gets a bleach bath just to be safe. :) I let it air-dry with the bristles up so it doesn't get gross.
This week I discovered another use for it -- I squirted dish soap on it like I would toothpaste and scrubbed out all the little bits of turkey and herbs that were stuck on the inside of my baster. :)