Annoying pet toys dose your cat or dog have one?  

my cat loves playing with the curtain in our kitchen. he also plays with papers. he loves playing with moving objects in general.

My dog has a squeaky toy that they love to play with. It can become annoying sometimes.

When I had a dog, a few years ago, I could guarentee evry Christmas one of my family would buy him a squeaky plastic toy. It would drive me round the twist.
Squeak, squeak, squeak. The worst thing I did was to ask my family not to buy squeaky toys for him.
So you can guess what they all did
Yip your right , everyone of them bought squeaky toys for presents, needless to say my dog loved them all. I did think about removing the sqeaky part, but my dog loved it, so I just had to put up with it.
It's only abit of fun after-all.

Oh yes, Sherlock definitely has an annoying toy that gets on my nerves. It was a present from my grandmother. It is a little toy rooster, that when something hits it, even lightly, it starts doing the c o c k a doodle doo (mylot wouldn't let me post the word all together). Barely touch the thing and it says that three or four times straight. And I have accidentally stepped on it, which renewed Sherlock's interest in it. I told my grandma she was ornery getting it for him.