I think the easy answer to the above question is to say: “Oh, of course you should. That’s just polite.”
But I’m not sure. I think it’s a question of social norms. I’m willing to do anything…as long as its the thing I’m expected to do. But, personally, my norm is that the host takes care of dishes and cleaning up. I’ve hosted tons of gatherings at my various houses and apartments over the year, and I never expected visitors to clean or was disappointed when they didn’t.
But social norms vary. And that’s okay. For instance, in Oakland and in Baltimore, the norm is that if you go over someplace, you should bring roughly as much alcohol as you intend to drink (in my case, zero alcohol). But in San Francisco and D.C., I do not think that’s the norm: you generally expect there to already be alcohol there. And both situations are okay. They’re responses to different social situations.
Anyway, last night, I was over at someone else’s place, and I drank some water and then just left the cup there on the table when I left, just like I always do (sometimes I’ll put it near the sink). But I am willing to start washing it if that’s what people honestly expect.