Why won't my cat play with toy balls?

Different cats like different toys. Some like toy balls, some like to chase a piece of string, some like those long rods with the big feather attached, some like toy mice, etc. You may just be trying the wrong toy.

And some cats just don't play at all. My aunt had a cat like that -- it just wouldn't play, no matter what toy you gave it. I think they usually need to be introduced to toys at a young age, in order to find them appealing. I heard that they have to be taught to eat mice by their mothers. If they grow up without a mother cat teaching them how to hunt, they won't know that mice are food. They will always chase mice -- that is instinctive to them. But if they haven't been taught that it's food, they won't eat it. They'll just kill it and leave it. So maybe a similar thing happens if they grow up without toys.

The best cat toy I've ever found is one of those laser pointers. Cats just love to chase the little red dot of light around. They're not very expensive, either -- like $10. And the best part is, you just get to sit on your butt and point the thing around. With other toys, like string, you have to run around with the cat. But with the laser pointer, you can be lazy while the cat exercises.