In Prisioner of Azkaban, Hermione buys herself a pet. She didn't buy an owl like Hedwig, a rat like Scabbers nor a toad like Trevor. She bought herself a cat in Diagon Alley out of sympathy that no one wanted him because of his squashed face. He has ginger fur, yellow eyes, a bottle brush tail, and squat, bandy legs.
He is part Kneazle and therefore has higher intelligence than normal cats. He recognized Padfoot and after much discussion, Padfoot (Sirius Black) finally managed to convince Crookshanks of why he was at Hogwarts. Crookshanks started going after Ron's pet rat Scabbers (who was really Peter Pettigrew in Animagus form) to try and bring him to Sirius. Of course, Crookshanks knew something was up from the moment he set eyes on Scabbers. This caused much rift between Ron and Hermione that year; Ron claimed that Crookshanks was out to get Scabbers from the beginning, while Hermione testified that cats chased rats. Because of his Kneazle background, Crookshanks doesn't like cheating, and he gives Ron and Harry disapproving looks when they cheat on their homework, reminding them strongly of Hermione. He likes playing with corks and watching them roll around.
I have my own Crookshanks. Morris came into my life when I was 15 years old. I convinced my mom to keep her. She has been my companion ever since. She is extremely possessive, jealous and attention seeker.
She likes to answer back when someone talks to her and has high intuition. She knows when I'm on the phone with Lex. Demands to be let in my bedroom when I'm at home.
She was my faithful compaion when I was writting my thesis project. I would be so lonely without my little Crookshanks/Morris.