All of my cats at one time or another have tried to open doors.

Back when Chessie and Casey were kittens, I initially let them in the bedroom at night. Problem with that was that Chessie would get up on things (nightstand, dresser, etc.) and start knocking things over, waking me up. Then the 4AM wrestling matches between the two of them would start. I'd be sound asleep, and suddenly somebody was getting body slammed into my stomach. I would shoo them out of the bedroom and close the door. That's when they figured out how to get my attention by reaching up and rattling the door knob. Keep in mind that this was about 3 years after my townhouse was broken into. So, getting woken up in the middle of the night by the sound of somebody messing with the doorknob would put me into panic mode. I'd open the door, and Chessie would take off down the stairs.

Casey has messed with the doors from time to time but nothing like Chessie did. Thankfully my townhouse has doorknobs instead of handles that they can grab.

Smokey also has a thing for closed doors, especially my bedroom and office doors. He'll wait outside either of the rooms, and as soon as I start to open the door, he'll try to rush his way in. If the door is closed and he wants in, he'll pound on the door and start crying his head off, sometimes trying to reach under the door.