Are you thinking of cases in which my enjoyment of a movie is ruined because someone has given me an unwanted 'spoiler'?

Not really, because this depends in part on human psychology, and we'd like to discuss more general agents than that. (Why couldn't other agents find out the spoilers, decide it's worth seeing, and then give themselves temporary amnesias so as to enjoy the twist ending? etc.)

I am thinking of cases where your seeking information has consequences. Cases like Omega are most obvious ('Omega comes to you and says he filled both boxes only if you would not ask for additional information' or something like that).

But they can be more subtle - for example, I've been reading up on price discrimination for one of my Nootropics footnotes, and it occurs to me that an Internet company like Amazon could snoop on your web history (through any number of bugs), assess your intellectual level and whether you comparison shop (receive additional information), and then dynamically adjust its prices to leave you with as little consumer surplus as possible - leaving you worse off than if you hadn't been receiving information.