My cat thinks he's a dog. He's a sweet boy.
I have a cat who plays catch with me (but only me - there are a lot of things that only she and I share). I generally use a small (smaller than a ping pong ball jingly cat toy, leather thingy) ball and she chases it down and rips at it for a bit, then brings it back for me to throw again.
Sometimes we use a rubber band. She gets bored with that game quickly, though. I think she is bored because she can't really beat the hell out of it when she grabs it. I brought home a huge rubber band from work about ten inches in diameter. She does beat on that a bit before she brings it back.
She also greets me at the door every time I come home, just like a faithful dog.
