I can't stand leaving dirty dishes out. I assume they'll attract all sorts of insects.
I had a college housemate who left all the dishes dirty, and washed what he needed. Drove me crazy. One summer, I was away for about a week camping, and he'd gone off to Europe with his mother shortly before I returned. I got back to the house to find that he'd left all the dishes dirty and piled everywhere. 90+ degrees, no AC, house all sealed up that way for a week ...
I washed the dishes that I owned, and took all the ones that he owned and put them in a trash bag in a trash can in the garage. When he got back a month later, he decided he'd rather buy new dishes instead of dealing with that bag. Only cured him of his ways for a couple months, though ... eventually I had to find a new place to live.
I'm surprised that we never had rats/roaches/mice with his habits.