Is it rare for a cat to play fetch?
I've a 16-year-old cat who loved to play fetch when he was a kitten, and a kitten who presently loves to play fetch with his spring toys--how unusual it for a cat to play fetch? I'd never heard of it before these two--thought it was limited to dogs--and whenever I've told people about it, they've never heard of it too, and even sometimes appear to doubt the verisimilitude of my story. Either I got really lucky or it's more common than most people realize.
One of my cats brings me a purple toy mouse (Whiskas branded, she is very picky about her toys) all the time and expects me to throw it away. She then runs after it, grabs it, cuddles it and brings it back to me, then I pet her and again throw it away. The "fun" thing about it is that I can hear her come with the toy by the sound of her growling :o) Her brother incidentally does the same. Indeed I never met anybody else with a cat playing fetch, but I don't know the answer to the question how rare it is. Maybe it is the owners who don't see the sign that the cat wants to play fetch?
Uncommon, but not rare. Chase-and-pounce is, of course, a widespread cat game; "retrieving" is the more complicated behavior.
Some cats figure out on their own that humans can be trained to throw a toy repeatedly if it's brought to them. One of mine does this. (Though it only works around a corner, since if she can see me she seems to get distracted and forget why she's carrying the toy.)
Cats can be actively trained to retrieve, but as with all cat training it takes a bit more patience and bribery to convince the cat that it wants to learn what you're trying to explain than it would a dog. That varies by breed and by cat, though; meezers, for example, tend to care more about human approval than most cats, which makes them better students.
My tortoiseshell does all the time, with zero explicit training on my part. She brings me a pompom or little mouse toy, drops it, then meows expectantly. She’ll even go as far as prodding my arm when said arm fails to throw it for her, and dropping the mouse even closer to me. It’s even getting to be a nuisance. This all started just spontaneously, when she brought one to me awhile back, and looked up at me.
"if she can see me she seems to get distracted and forget why she's carrying the toy" My cat does get easily distracted too but I noticed it often drops the toy when I make eye contact. Staring at the ground when the cat is retrieving something seems to work best to make my cat drop the toy in front of me.