What strange or interesting games does your dog play ?

That's interesting because my dog likes to play something along the similar vein.
Once my dog had accidentally knocked over a lamp. Nothing happened except for the bulb breaking, but the noise had convinced my dog he had done something really, really bad. My brother happened to be there at the time. So the next time he comes, my dog pounces on him with joy and bro dearest asks him, "You fixed that lamp, Gus?" I don't know how Gus understood or remembered, but he got off bro all of a sudden and settled down to casually lick his paw, occasionally darting glances between the lamp and me. The first time we were just simply stunned by his reaction.

Ever since my bro gets a kick out of asking Gus about the lamp and Gus for his part oscillates between angelic innocence and stout denial, all the while glancing at the lamp and me. (He doesn't go anywhere close to it anymore)