Enter a great idea from cousin Kelly via FlyLady.
If you don't have a dishwasher, don't worry. A dishwasher is just a dirty dish disposal. Clean out a place under your sink and put a dishpan in there. Teach your family, that instead of putting their dirty dishes and glasses in the sink, place them into the dish pan.
It's amazing how effective this is. Now our sink is always empty. And doing the dishes each night is a fun family chore. And our kitchen stays super clean.