Name: Sasami Masaki Jurai/Tsunami-kami-sama
Occupation: Princess of Jurai/Goddess -in - training/Cabbit abductor
ORIGINS
Sasami's origins are often two-fold. On the surface she is" the little sister of Ayeka", as Noboyuke Masaki introduces her in the Tenchi Universe series, and for the most part, this is a lot of who she is. But although Sasami Masaki Jurai is a little girl, she has connections and bonds with something far older and more powerful - the Goddess Tsunami-kami-sama.
The connection between Sasami and Tsunami only appears in a tangible sense in the OVA series, although it is spoofed upon in the Pretty Sammy series (in this, Tsunami is the Queen of Juraihelm and Sasami her unfortunate assistant on the Earth to try and restore the balance of magic). In the OVA series, Sasami's union with Tsunami is explained by Tsunami - that when Ryoko attacked Jurai under Kagato's control, Sasami was almost killed. By assimilating with Tsunami, Sasami survived her fall and remained alive (although Sasami herself is confused about her origins and believes Tsunami created her, rather than saved her life). It seems very likely, however, that Tsunami simplified her connection to Sasami when she explained it to Ayeka and the rest. This is because Sasami resembles Tsunami even before they are assimilated, which suggests that Sasami was probably born Tsunami's chosen one, and that Tsunami used her magic to save her protegee, rather than just to save a Princess's life.
As Tsunami, Sasami has control of Jurai's most powerful spaceship, Tsunami-fune, which is capable of producing the ten wings of the Light Hawk (the universe's greatest - apparently - magical force). Sasami herself does not seem to manifest the Light Hawk Wings herself...she prefers to rely on Tsunami to do it. However, her connection to the Goddess gives her other magics as well, including that of precognitive dreams and the ability to use her magic to heal (again through Tsunami and the magic of her ship).
And yet, at the end of the day, Sasami is still the daughter of the Emperor of Jurai, Azusa, and his wife Misaki (whom she bears a striking resemblance to, also!). She is Yosho's half-sister in the OVA, and Ayeka's full sister. This also makes her Tenchi's great aunt, and that's just disturbing on all and every level to anyone wanting to marry those two off to one another :P Her name is Masaki, like Tenchi's, because in the OVA, the whole of Kurashiki in Japan seems to be populated with Juraian born immigrants. And as I said, they are closely blood related.
In Tenchi Universe, Sasami's background is a bit more obscure. There is no mention of Tsunami or even an Emperor or Empress she can be descended from in this series, although we know she is a Princess of Jurai. Ayeka is still her sister, but Yosho is no longer her half-brother and so she is of a less important royal family than the direct line to inherit Jurai's throne. She also has an Uncle who is a military commander and who cares about her enough to help her escape when they are fleeing Jurai ships in an attempt to clear her name. How he fits into the family tree is unknown.
In Tenchi In Tokyo, Sasami's background is largely the same as it is in Tenchi Universe, with her being the sister of Ayeka but not the sister of Yosho. Again, her parents are unknown.
In the Pretty Sammy series, Sasami is an ordinary Earth school girl of about ten years old, who is suddenly chosen by an alien queen to carry out her magical bidding. In either series she is part of a different family - in the Pretty Sammy OVA she is Tenchi's younger sister and no relation to Ayeka at all. In the TV Series she has no brothers or sisters and isn't related to any of the regular cast.
In Mihoshi's Special Episode, Sasami has a Pretty Sammy moment, as well as being a young and eager apprentice police cadet who makes the best tea in the force. Anything else about her background in this episode is pretty much unknown.