I was not a big fan of the hurricane in Ohio. That was not my idea of a good time. It's one thing to watch something on TV and go "ooh, badass", quite another to be standing in a mall parking lot, watch a row of high-tension power lines collapse over a busy street and hear people screaming, and then watch the giant transformer that services the mall explode. Then trying to get home alive while watching the top being ripped off the gas station shelter and more transformers exploding right and left.
We had a big tree down in our backyard. I told our landlord and he didn't do a thing. We finally had to borrow a saw and do it ourselves. Incidentally, not a big fan of the landlord either.
I have a friend whose landlord also did nothing about a giant felled tree in her front yard. The city took care of the bulk of the tree, since it went over the street, but she was left with a 6-foot ragged stump and it's still there 6 months later. She decorates it for every holiday.