I frequently lament the fact that I have no dishwasher. One of the worst problems I face, that can't be remedied by soaking in a white vinegar/water mixture, is coffee stains in our mugs. I can scrub them with soap as long as I want, but they don't come out. There are a couple of chemical products that work, but I dislike using them on surfaces that touch our food. So, here's the fix: Mr. Clean Magic Clean Eraser. You wet it, squeeze out the excess water, and rub it on the inside of the cup. No scrubbing, no elbow grease. The coffee stains literally wipe right off.
If you have a dishwasher that does this for you, I hate you just a little bit. :)