One of my cats does. Patches is 3 1/2 now and he doesn't do it as often now but up until 6 or 7 monthes ago that was a daily game. These are my first cats and I didn't know cats would do that. I thought only dogs did it.
Jaffa does it. He goes round and round in circles and he often does it when he's sitting on a platform on his cat tree and has been known to fall off! I've never seen Mosi do it (other than general kitten swiping at the end of it if he catches sight of it) and my bridge babe Magpie never did it.
My Annabelle chases her own tail, it's so funny she acts like she's never seen it before
Gracie and Lizzie chase each others tails and Kidd, well he's fasinated my Lizzie long bushy tail and TRIES to chase it...Lizzie swats him but still he comes back for more!
My 11 year old cat Tegato chases his tail still occassionally. It is hillarious to watch. Fortunately he does not growl or play rough with it. He will use chase it for a short time and eventually hit lays down and starts cleaning his tail.
We never have the camera ready, but PJ is a major tail chaser. She pirouettes and spins around, getting lots of air under her. It's absolutely fascinating to watch her to do, and it's all we can do to keep from laughing like crazy and making her self-conscious. She's especially fond of chasing her tail when she's up against something - a wall, a table leg, or even when she's sitting in a box!
Yes, Palekana still chases her tail and she is 8 years old. Every once in a while she'll look at her tail as though she had never seen it before and start chasing it crazily. Eventually she calms down and starts licking it. Silly girl. None of my other cats do this. They outgrew it long ago.