Ayeka:

Ayeka is the first crown princess of Jurai and heir to the throne.  She ends up living with Tenchi on earth after her attempts to arrest Ryoko went more than a little bit wrong, when Ryoko caused her ship to crash, leaving both Ayeka, her sister Sasami and Azaka and Kamidake (Ayeka's guardians) stranded on earth.  

Ayeka is very stubborn, she is a royal and she knows it.  Her sense of humour is, er, almost non-existent, and on occasions she has shown that she can be quite the little schemer.  before she became stranded on earth, (about 700 years before), she was engaged the her 1/2 brother Yosho, the first crown prince of Jurai, (on Jurai, it is not unusual to marry your 1/2 brother, maybe they saw the ancient Egyptians and thought they would copy or something).  however, Yosho went missing and was presumed dead after a battle with the "evil" demon and space pirate (guess who).  Ayeka was devastated and began searching for her brother. 

She is ALWAYS fighting with Ryoko over Tenchi (among other things), whic is a bit strange concidering she is really Tenchi's great aunt (eww).