Here's the first cabbit to achieve gosu stardom: Ryo-Oh-Ki! Winner of the 99 Anime Expo's title for best non-human character and inspiration for a line of plush cabbits, Ryo-Oh-Ki has earned a place as my favourite anime personality.
Ryo-Oh-Ki serves as comic relief in the sci-fi comedy Tenchi Muyo; in a way, she plays Pikachu to Tenchi's Ash. She makes her first appearance in the third or so episode of the Tenchi series, hatched from an egg than purportedly came from Ryoko. Sasami quickly warms to the cabbit and the two of them form a tight pair for the rest of the series.
Ryo-Oh-Ki has a variety of powers at her disposal: abilities to both fly and morph into a spaceship capable of interstellar travel. In the Tenchi OVA series, she even exhibits her skills of shape-shifting into a three-year-old cabbit/human version of herself! Her only weakness is her willingness to use any means to attain her favourite food: carrots.
Being a rabbit-cat mutation, Ryo-Oh-Ki sometimes expresses herself a manner typical of both those animals. She'll unhinge her claws and assume a menacing, cat-like posture when she feels threatened, but she can also become sympatheic and concerned when she senses that a friend of hers is downspirited. All in all though, Ryo-Oh-Ki makes for a very cool character, one whom I'm sure many pets can identify with ^^;