Hair
One of the things he hated most about his scar was that, when he got it, he lost his hair, too. Nearly all of his gorgeous black locks were gone, save a small topknot on his head. Then he met Aang and Sokka, who were also bald, and decided that maybe not having hair wasn't so bad after all. (besides, Katara seemed to like guys without hair.)
TattooHe has a small tattoo on his ankle that no one knows about. He hides it shamefully; no one but Uncle and Father know it's there. It was marks him; it proves his exile against the Fire Nation. When he joins the Avatar, however, he shows it off proudly, and years later, whenever he is crowned Fire Lord, he demonstrates the serpent-flame tattoo with pride.
NecklaceHe doesn't know whom the necklace belongs to, and he finds it hard to care. He just never expected it to bring about such a connection between him and the Waterbender, and to this day, believes picking up that necklace was the best thing he ever did.
ArmorThe gleaming red of the Fire Nation armor was something he was oh-so-very-use to---he just didn't think he'd ever hate it as much as he does now.
GameHis Uncle is a lover of games---pai sho, for example---the old man could play games endlessly. Zuko is only fond of one game, the game he's forced to play, and even Cat and Mouse gets dull after a while when the Cat is too tired to care and the Mouse is naïve enough to believe the Cat isn't going to eat him when he's finally been caught.
GangHe wasn't use to traveling in such close quarters with only three other people; three people of whom he had to be in contact with and had no such authority over. It was this, over anything, that made him accepted in their little gang. It had made them family, in the end.
Storm
He's never forgotten that storm, when the winds were destructive and the sea was raging. It was in the same storm he proved he wasn't so bad anymore.
MoralsIt was pretty sad. He was the only one along this sad bunch of 'heroes' who had any morals. The girl was a thief, the Avatar a pathological liar, and the water tribe boy, Sokka…well, Sokka was an idiot, so he didn't count. Zuko never counted idiots.
EyesHe didn't care much for his eyes---even before the scar, he didn't like them. The scar only gave him more of a reason to avoid them.
BookHe loved books. It was something strange Katara found out about him later on, after she got to know him. Every time they had a chance, he would pour over a certain book he carried with him, allowing himself to get lost in the fiction of the pages. It must have been a good book, because he hasn't met her in the eyes since.