I used it briefly to log the food orders in Pokemon X/Y. Other than that, I don't bother using it. I know some people include contact information in them in case it ever gets lost.
I write down my last played day in Animal Crossing I hate missing even one day so I like to know what day to start with again. I also write what I call to be the last "safe" day to play Animal Crossing. By that it's just the last possible day I know that I can play without anyone moving out.
I am also a total nerd and use another note to keep track of what episode of the Pokemon anime that I'm on. I started with season one and plan on watching them all in order until I either catch up to current day (season 17 I believe) or just get tired of it. XD I'm currently on season 6 the first season of Hoenn.
I didn't even know anything about them until I read this thread. Maybe I'll start using it to make a note of the last day I played ACNL so that I can take breaks from playing it without worry.