I'm glad to see I'm not the only person that doesn't wash them, I've wondered if I was horrible for that. My dogs leave no residue in their dishes. I feed in their crates, so I just leave them there until it's time for their next feeding.
The water dish, I usually rinse out before refilling, and if it's looking icky (which does happen), I clean it out with dish soap and a scrubby sponge. It doesn't really fit in the dishwasher. They also have water dishes in their kennels for when I'm at work. They tend not to drink out of them very much, but I do get them out and clean them sometimes, they get slimy otherwise.