is it just my cat or other cats too?
my cat tries to mimic what I do, she eats her meal when I eat mine, she tries to be with family when we all gather up, she tries to go out when I go out, she attempts to come in to the bath tub when I take bath, and when I climb up the stairs she does the same.

Some cats just want to be where the action is and know what's going on all the time.

We have a cat that, when we first let her in the house, cried at us because she couldn't get into a closed door and check everything out.

Your cat just sounds like she's attached to you. Not a bad problem if you ask me.

Some cats just want to watch the world burn.

Forgot to respond to your question earlier, Texas ~ No, i didn't train my cats, but i have to admit, part of the reason i'm starting to suspect why they do it is because I give them food everytime they go to the closet. But i don't overfeed them =P

and my cat want to watch my burning love toward her



my cat isn't big eaterry cat and I think that's gonna be challenge for me.

and Folks Cat and dog foods are not for your healthy breakfast.

A friend of mine had a cat that hated to have it's belly rubbed. The best game to play was to put on a thick leather glove and scratch his belly with it. He immediately started to scratch and bite, but when he realized that he was not winning, he lets out a low yowl and runs off.

My cat too. she just can't out stand with her belly being rubbed. she used to like it before but not anymore apparently.

hummmm
http://www.youtube.com/watch?v=h6a8T5Z5wkk
https://www.youtube.com/watch?v=yAKw6yGwOH8
these may look odd to some of you folks.
I do this to my cat and she enjoys it. and I think this is only for cats not dogs. and I don't do it as hard as in the videos, just lightly..

I'll accept any and all tummy rubs your pets don't like.

My younger dog doesn't dislike tummy rubs specifically so much as being upside-down confuses him. *giggles*

My cat loves belly rubs, its adorable

Polydactyl cat

some cats have thumb(s)!

That's kinda creepy and weird looking.
One of my cats, she can grab things just fine with her tiny paws. If she had thumbs she'd probably be opening the fridge, and many other things that hide food.

My Akita's getting old. He still likes to play though, but he doesn't feel well a lot of times.

does her occasionally hide somewhere dark, closed, or undisturbed?

He doesn't really do anything like that, it's just that sometimes when he doesn't feel well or whatever he doesn't like to be bothered. Of course, he is an Akita, so he doesn't like to be bothered anyway. Lol

Presumably they don't work like thumbs, though.

no, if a cat can give you a thumbs up, they are working like thumbs.
https://www.youtube.com/watch?v=2hngBzDDyFE

I played a youtube cat video while my cat was on my bed, as soon as she heard a meow from the video she started to growl and stare out the window to see if there was a cat out there.

If cats develop thumbs, what is going to stop them from taking over the world?

No one!!
but My cat needs thumbs..