The state of Oregon owns and operates about 28 small airports and says: "We also encourage you to use the "sign in" boxes we have at some of the state airports. This allows us to better assess the level of use at some of our smaller airports." (http://www.oregon.gov/Aviation/Pages/warning.aspx)
No doubt its department of aviation uses the visitor register for feedback and as one more item to show that there is enough traffic to keep the airport open. I now make it a habit to see if there is one when I fly into a back country airfield and sign it and comment. First time I thought to did this I couldn't think of any useful comment.
