My first cat - who was by all accounts the stereotype of a highly intelligent Siamese - would play fetch, catch, ping-pong ball football, hide and seek, leap-up-and-grab-the-toy-out-of-my-hand, turn the bathroom light on and off and so on. I even managed to train her that the most effective way to get food was to sit cutely by her bowl rather than tripping people up, mowling or jumping on the surfaces! We're forever grateful that she never learned to answer the phone (my aunt has a Siamese who was notorious for this, so their line was often engaged) or flush the toilet.
Sadly none of our subsequent cats demonstrated anything like that level of trainability, though one of them did have a favourite ball that she'd carry around (sadly, even to the litter tray) in her mouth and throw at you when she wanted to play. And another managed to train both the humans and the local squirrels to be a source of entertainment (squirrel would appear at the window, cat would go and get attention of humans, humans would throw nuts to squirrel, cat would sit and bark at squirrels eating nuts).