Arnold is always seen wearing his small blue hat.
Arnold's parents bought him his hat when he was just a baby (as seen in "The Journal") and he has worn it ever since.
In "Arnold's Hat" Arnold is shown to be emotionally attatched to his hat to the extent that he refuses to leave his room without it. It can be inferred that the reason why Arnold is so attached to his hat is because his parents, whom he misses and still loves, gave it to him.
Times when Arnold is not wearing his hat
This category focuses on times when Arnold was wearing a different hat, his hat was covered, or he took it off.