Cats do NOT like to be on the wrong side of doors. If I shut mine out of a room, they'll whine and yowl til I let them in. One has even taken to rattling the door by slipping his paw underneath and shaking.
Apparently my dogs freak out when I have my door closed [which is all the time] so they always barge through my door to open it as much as they can, then stand in the door way look at me for a few seconds and then proceed to leave. It sucks my door lock is broken so I can't actually close my door all the way.
My kitten left for a few days to stay at my boyfriend's, when he came back my dog finalyl acknowledged his existence, cleaned him, followed him... just for two days. He's gone back to ignoring him now.
My cat reaches under my bedroom door and waves her paw around, as if hoping that somehow, with the opposable thumbs she doesn't have, she will be able to grab me by the ankle and pull me out through the gap under the door.
My cats hurl themselves against the door until it opens on its own or I let them in, or they'll reach under the door and tear at the carpet. They're not happy unless they're in the same room as me. It's sweet, but annoying and sometimes kind of creepy.
I'm really glad they haven't figured out how to open doors yet. I can imagine going to the bathroom when suddenly the door opens...