It's funny, but the one cat we have who does that is stodgy, grumpy old Ace. (He's not really old, only about 10, but he's kind of "grumbly," if you know what I mean.)
He doesn't play much, but if he happens to see his tail curled up against a wall or something, he'll bat at it and chase it for a bit.
Occasionaly she will stare at it with this look of "What the? Why does this thing keep following me around? I'll show it!" and around and around she goes.
My older cats only chase their tails when they've gotten ahold of the cat nip.. but my 5 kittens are all about the tail chasing!! They are sooo cute too because sometimes they will all be chasing the same tail.