Wow! I thought our cats were a bit odd, but after reading these other posts, I'm beginning to think they're more on the normal side!
I think the funniest things two of our cats do, involves the living room celing fan. They'll walk to the center of the living room... happen to look up at the fan, which has a mirror behind it. Evidently they see the "other" cat up there on the ceiling, flickering in and out between the fan blades. They'll sit there with their heads doing that circular motion, which has my husband and I rolling of the floor! But, after about 5 minutes... either all the eyeball/head rolling gets them disoriented OR they just can't figure it out - but they'll start freaking out. They'll hunker down... then slink off to the side, all the while keeping an eye out for that cat on the ceiling. Then they'll run off. Come back and skirt the edges of the room, to stay away from the cat on the ceiling. About an hour or so later, they forget all about the "other cat"... and everything's fine for about a week or so. Then, the process will start all over again. The weirdos.