Ryoko is a semi-reformed space pirate who is madly in love with Tenchi Masaki, the main protagonist. She is always shown to have a very competitive relationship with Princess Ayeka, who also has a very strong romantic interest in Tenchi. Ryoko has differing abilities between the different continuities (the OVA, Tenchi Universe and so on), but her aggressive, emotional personality tends to remain the same.
Ryoko is the product of combining a powerful creature known as Masu, with the ova of Washu Hakubi, the greatest scientific genius in the universe, making Washu her mother. Ryoko was created to be an entity capable of wielding the power of Washu's three mysterious gems. Washu, who is one of the Chousin—three deities who created the universe—descended to the third dimension and placed her power into the three gems. Washu also created a living spacecraft, the powerful Ryo-Ohki, to be Ryoko's companion and ship.
However, Washu was sealed away on her powerful battleship, Soja, by her assistant Kagato. Kagato then enslaved Ryoko and claimed her as his own, using her for his own personal gain. Ryoko, under Kagato's control, decimated 28 planets and 69 colonies.
In order to capture the power of the goddess Tsunami, Kagato had Ryoko singlehandedly attack the planet Jurai, whose royal family are the only ones to hold the secret of Tsunami. Ryoko, along with Ryo-Ohki, nearly decimated Jurai, as their power was mysteriously equal to that of their extremely powerful Royal Treeships. In order to defeat her, Jurai's Prince Yōshō chased her all the way to the planet Earth, where he managed to subdue her and trap her in a cave near the Masaki Shrine by stealing the three gems.
Seven centuries later, Yosho's grandson, Tenchi Masaki, incidentally frees her from her imprisonment. For seven hundred years, Ryoko felt trapped within the cold, damp loneliness of the cave and wanted to have a little "fun" at Tenchi's expense by attacking him, which she considered play time, destroying his high school in the process. Fortunately, Yosho's Master Key, Sword Tenchi, (which doubles as a light sword) was also in the cave, and it helped Tenchi disable a gem fueling Ryoko's abilities.
Afterwards, Ryoko begged Tenchi to relinquish one of her gems which Yosho embedded to the palm of his Master Key so she could re-awaken Ryo-Ohki. This happened to be just in time, for she had sensed Yosho's sister, Jurai's Princess Ayeka, approaching Earth in search of her lost brother. Ayeka indeed proved threatening in her own search for vengeance. After a battle, both Ryo-Ohki and Ayeka's Royal Treeship, Ryu-Oh, crashed on Earth near Tenchi's home - leading to Ryoko becoming a permanent house guest alongside Ayeka and her little sister Sasami.
Also, fortunately, her ship managed to regenerate in a way - a reincarnated Ryo-Ohki entered the scene, with just as strong a bond with Ryoko as the former.
As for Ryoko herself, her feelings for Tenchi emerged themselves, and thus she and Ayeka opened a new chapter in their long rivalry - since Ayeka believed Yosho to be dead and was stranded on Earth, she was forced into proximity with Tenchi and Ryoko. She developed her own feelings for Tenchi - leading to a legendary feud between the princess and the space pirate.
Technically, Ryoko is a free woman. Her criminal files have been erased due to statute of limitations. Ironically, being imprisoned for so long helped lead to her overall freedom, since she can no longer be charged, which was all apart of Yosho's plan. Just as well; Ryoko is a free spirit who hates responsibilities or other restraints. When it comes to her relationship with Ayeka, the two of them are polar opposites in personality, as well as archrivals for Tenchi's affections. In regards to prominent character traits, Ryoko is very emotional. She easily gets upset, and is incredibly short tempered. She is also very raunchy and sexual, especially when it comes to Tenchi.
Due to her former life of being used purely for destruction, as well as her long imprisonment, both cutting her off from traditional interactions, Ryoko has little concept of what is and isn't "socially acceptable". This would explain why she has no problems with sexual displays, is persistently either highly volatile when criticized or passive-aggressive when someone tries to impose authority, and shows few signs of any impulse control. Typically, Ryoko is very mercurial - she's very carefree and laid-back most of the time, but is easily identified by her dangerous temper. However, when Ryoko encounters something that truly scares or saddens her, ranging from insults about her age to seeing someone important to her in danger, Ryoko can be very prone to tears.
Ryoko is also sometimes rather childlike, and can be a bit gullible. Since most of her life was spent either working under Kagato or sealed inside a cave, she does not have much experience in "normal" situations. Overall, it seems that many of Ryoko's negative traits - like her unabashed sexual behavior and impulsive, aggressive actions - might not be from actual malice, but perhaps from a lack of social interaction. In the True Tenchi novel "Yosho," it is revealed that while under the control of Kagato, he tried to squash all emotion out of her, and she attempted to receive some sort of emotional interaction from wherever she could get it from; even sex and masturbation didn't cut it for her. Attacking people and the things they cared about was the only way she knew how. Ryoko is also extremely sensitive about her age, being brought to tears when Ayeka called her a mummy - although it should be remembered that Ryoko was quite drunk at the time, her age still seems to be a sore spot.
Ryoko is deeply in love with Tenchi, though not fully admitting how deeply until Episodes 5 & 6, when she tells Ayeka how she first met Tenchi, and later when she offers up her own life in place of his. While she was trapped in the shrine, she was able to create an astral body (a ghostly body piloted by her consciousness) and venture to the entrance of the cave. She watched Tenchi grow up over the years, and she wished more than anything to be with him. In fact, it was Yosho's plan all along for Ryoko to come in contact with Tenchi while sealed away; by experiencing childhood through him, it would change her for the better. However, the way she introduced herself to him was terribly frightening to Tenchi, so he distanced himself from her for a long time. Also, when Washu is first introduced, she tells Ryoko that she knows how she feels about Tenchi and says that Ryoko wants to do "this and that" with him.
Ryoko has a bit of an ambiguous relation with Washu, her mother. When Washu first appears, she critiques her daughter's sex appeal and asks Ryoko to refer to her as "mommy." As the series progresses, she starts to fear Washu, especially when Washu starts doing some of her experiments on an unwilling Ryoko. In fact, Ryoko becomes slightly cautious whenever Washu is looking at her with a mischievous smile and intimidating eyes. Their mother-daughter relationship is played upon several times as Washu shows equal or greater sadism than her daughter such as making degrading comments about Ryoko's physical appearance.
Washu does what many consider to be cruel, harsh things to Ryoko, however, this is the only real way to get through to Ryoko, undo the damage that Kagato did to her, and soften her up so that she'd be a better pairing with Tenchi. The most extreme example of this mother-daughter sadism as well as Washu trying to get Ryoko in touch with her own emotions is when Washu, knowing Ryoko has a fear of being trapped in cold and dark places, leaves Ryoko bound in her lab. After a single night, Ryoko breaks down and begins crying, calling for her "Mommy" over and over while Washu records the incident, commenting on how cute Ryoko is and the "pleasures of motherhood." Despite this, the two do share more parental moments such as when Washu states that she will not force Ryoko to assimilate with Dr. Clay's robot Zero who became Ryoko's complete copy and does not limit her show of the emotions that she incidentally duplicated from Ryoko, but possibly because of a grudging respect for Washu or simply because she wants to, Ryoko agrees and now is more in tune with her feelings and acts more human. Not to mention, her knowledge has been enhanced after fusing with Zero.
Perhaps the most telling sign of a deeper connection is the simple fact they have a mother-daughter relationship. Even though Ryoko is essentially not Washu's daughter by birth, Washu still refuses to consider Ryoko a mere creation for personal uses; always her daughter. This can also be seen in Washu's conversation with Juraian empress Funaho, where she declares she would never create another Ryoko who will always be her only daughter. It remains rather clear that, despite Washu's on and off antagonization of Ryoko, she still loves and respects her as a daughter in the end.