Jim’s cat with her usual attitude. (“You woke me up to take a picture? Don’t make me kill you.”)
My cat with her usual attitude. (“Play with me! I’m silly! Play with me!”)
There ya go. 
First of all, thanks for letting me join the board. I have read here forever and love it.
Now, on topic, I know a cat who can fetch little toys, sit, stay, and roll over to name a few. Her human is a dog trainer. My own cat likes to get in the desk chair and let me spin her around. She taught me that. She can also disappear into an alternate universe when it is time to go into her carrier to leave town. That’s about it.
There’s a show in Las Vegas featuring SEVERAL trained house cats. Gregory Popovich picks up cats (and a couple small dogs) from the shelter and trains them to do circus tricks. He’s got a very entertaining show. Wanna see something impossible in Vegas? Forget the magicians. Everybody knows it’s impossible to train a house cat. Here’s a clip of his act;
Enjoy!
Visitors are trained for one cat and another cat raids your neighbor’s kitchen. These cats are AWESOME! 
There’s no doubt that Fatcat refuses to listen. But it’s okay since he’s cuteness personified.
Whoa! When a cat looks at me like Jim’s cat in that pic, I would jump to obey her waved command and open the door!
Housecats can definitely be trained, but I have difficulty making the trick reliable. They know how to do it, but won’t do it unless they’re in the mood. Arthur recognizes his name, he’ll come when called, he’ll stand on his hind legs, and a variety of other things, but sometimes he just doesn’t feel like it. Rodeo is good at opening doors, but only when he wants the door opened.
I’m especially proud that I’ve taught Lena not to rip my face off when I trim her claws.
I can teach our cats not to do such things when I’m in the room. Snowball likes to take my spot on the couch. I walk up, look at her, she moves. But as soon as I leave the room, she’s right back there. I can get Shadow to leave my room when I say, “out,” but I can’t get him to not go in there in the first place.
I had a couple of koi that would come when called. They’d come to me at the edge of the pond, and I’d put some food pellets in my fist and lower it in the water. They’d put their mouths over the circle of my forefinger/thumb and suck the food out. They would also let me pet them.
Funnily enough, she’s actually very affectionate. She just happens to have about five cats’ worth of attitude in one little body.
Nice picture - “Do you think this hat is too much?”
When I first read that sentence I laughed so hard I almost fell backwards off my chair. But whilst typing this reply I noticed there’s a “not” in the sentence as in “not ripping your face off”.
Spinny will tap you on the shoulder to get your attention. She did it (to me) when some family friends were here, and they thought that was the cutest thing.
Jezabel will play fetch with the little yellow foamy earplugs - no other kind or color, it has to be the yellow ones.
She likes to lay on the end of the bed beside me while I am at my computer desk, or lay beside me on the bed when I am using the laptop on a hospital table, and she will gently pat me on the arm with her paw if she wants some attention.
She will sort of do her version of dance dance revolution on the edge of the bed if she wants mrAru to pick her up and dance around with her upside down [like you are cradling a baby, and doing that little baby dance thing]
She will do these even if it is someone else in my chair or standing by the bed - we usually have to explain what she wants. She looks adorable carrying the little yellow earplug around in her mouth … I really need to get a picture of it =)
Good luck with that - Jim’s cat, Max, drags a net bag of foam balls around, up and down the stairs, for reasons known only to her, and I think we have one fuzzy picture of her doing it - she drops the balls as soon as the camera comes out.
Sirius Black will sneak into the bathroom and give your butt a little nip when you’re perched on the toilet but I most certainly did not teach her to do that.
I don’t discourage it though…
Our cats learned to talk from us.
It was about 6 months after they adopted us that I thought about all the noises they made, and finally recognized that they were talking to US. They never talk like that to each other, just to US when they’re trying to ‘say’ something. (Something like 'OMG I’M SO CUTE HOW CAN YOU NOT GIVE ME YOUR PEPPERONI?!) whatever…they simply do not meow at each other, ever. The occasional growl or hiss as they’re playing, the usual…but the chatty kitty-talk is directed at humans, and only humans. Maybe it’s a big ‘duh’, but I thought it was pretty cool. 