Emmy has an obsession with Lazer pointers, balls, speakers and squirrels. Zuri and Akasha have an obsession with food LOL. Bailey has an obsession with a round cat toy that holds a ball....
I think most dogs, if not all, would be inclined to like, if not be obsessed with balls!
My Cruiser likes tennis balls and another gummy ball I got him a few months back. He likes to have the balls every time we go out.
My parents have four little dogs 2 shih tzu, 1 lhasa apso and one is a shih tsu cross (not sure what the mix is). Only one of them likes ball games, the others just look at you as if to say 'fetch it yourself!'. One of their dogs loves squeaky toys and another drags a teddy bear around with him.
We once had a terrier who loved squeaky toys, she would play with her squeaker for hours, it was enough to drive you mad!
Jasper doesn't seem to have any obsessions yet but since he's young, he does love to play. LOL
Rocky seems to be obsessed with chasing our cats. They have clawed his nose a couple times when he got too close but that doesn't deter him.
Most dogs soon learn how far they can go with cats, but one or two are slow learners and the get one or two 'war wounds' before they learn!
Rings? do you mean the type that you wear on your fingers? If so that could become an expensive obsession.