I love cats playing fetch! Poppy doesn't get it at all, just looks at me when I throw something, but Monkey loves it! Sometimes he plays just for fun, but most of the time he comes with a toy in his mouth, ready for play... when he wants to interrupt me doing something, especially if OH is there. (Ever the attention seeker.) Still, he looks so cute that I always drop whatever I'm doing to play with him instead. Well, anything to stop the howling.
Helen, I do the same thing - throw a toy away from front door when going out. I always make sure it's a toy Monkey can't carry in his mouth, though (ping-pong balls, normally!).