When I was in middle school and high school, I had a pet rat. His name was [broken link! FIXME] Fnugus. I saw this video recently that made me remember that indeed, my rat was a pretty smart rat.
I had trained him to go to his cage much like the girl in the video. He would also jump whenever I said "jump rat." If I did it several times in succession, it made him look like he had a weird tic or was spastic. That was entertaining. It was also fun to put him on some elevated platform and have him jump to another platform. He would jump back and forth.
Mostly when I was in my room, I would allow him free run of my room. After he died, I found he had built a secret nest behind a filing cabinet in my room. It was full of some of my drawings, shredded into a comfy bed. I didn't hold it against him.
[daily log: 2 hops and a jump]