Possession is a topic in and of itself, so not including all of the scenarios in which you think you're likely to be possessed next turn, or you're possessing someone and you don't want to play it so that their next turn sucks.
There are "theoretical" reasons to do any of the below that many of the others have already mentioned. In my many (over 3000) now, games of dominion, i'll try to recall scenarios in which I've actually done these, to put some sense on practical.
(1) Return Treasury to the top of your deck when you have not bought a victory card?
(2) Return Walled Village to the top of your deck when you do not have more than two actions in play?
(3) Return Alchemist to the top of your deck when you have a Potion in play?
The most common reason for these would be when masquerade is in play, and you don't want a hand full of good stuff to be stolen. Walled village is new, and I don't think I've ever not done it. There have been times when I've agreed with those who said they wanted their +actions to be in the deck so that the golem can find them - but I think that those instances are probably not optimal play.
(4) Not reveal a Province after playing Explorer?
Never done it in real life. My best thought would be a hand consisting of Gold, Gold, Horn of Plenty, Province, Explorer - and really wanting a 4 cost card instead of a 3. Playing explorer is already an edge case. For those who mentioned menagerie... just play the menagerie first! (Unless you have 2 explorers, but now we're just being silly)
(5) Not discard a Curse to circumvent a Mountebank attack? (I guess there's one reason for this: you're ahead, and taking one more Curse or Copper will end the game. Any other reason not to do this?)
Another reason would be if having the card in your hand has value. For example, you have a cellar or a warehouse, and you want to use the curse in your hand. If I've ever done it, it was to end the game though.
(6) Reveal a Province after playing Tournament? (There's a thread in the Puzzles forum about why you might not want to reveal a Province to someone else's Tournament.)
Never done it in real life. The answer of "all prizes gone" and I need the next card to buy the last province and end the game instead of a duchy sounds valid enough.
(7) Choose a location for Stash on the reshuffle?
This is reasonably common. I actually did this yesterday in a retarded game with a crazy King's Court / Torturer / Bazaar / Horn of Plenty action. I wanted the stash to drive up the ability of the horn of plenty, but I didn't want it in my hand, so I put it at the bottom of my deck. Any time you're reshuffling mid hand based on what you've already drawn and how many cards you have in your hand, you might not want your stash. (Example, you've already drawn Gold, Gold, Silver and there are no sources of +buy)