A neighbor fell off my porch the other day and he had to be taken to the doctor with a broken arm. Can I be held responsible for this?
Only if it is determined that you did not keep the premises in a reasonably safe condition for him and other guests on your property. Therefore, it is important to understand how he came to fall of the porch. Did the railing break? Was it rotten? Did he fall over the rail? Was he sitting on the rail? Was there no rail there at all? Did local building codes require a rail? And so on.
There are all sorts of questions that must be asked to determine whether you can be held responsible for what happened.
You should promptly call your homeowner’s insurance company and advise them what happened. You should also take pictures of the area where the fall occurred and write down the names of everyone present.