In this series, Ryoko is a space pirate who was defeated by Yosho nearly 700 years before her release by Tenchi.  Before that, she was a slave to Kagato.  Her physical age is 17 years old, but her real age is over 2,000.  She was created by Washu, using her egg cells as a base, so she's indirectly Washu's daughter.  She has three power gems that are the source of her energy, which were also created by Washu.  The gem on her left wrist allows her to summon a demon, the gem on her right wrist allows her to control the demon she summons, and the last gem, which goes on her neck, gives her full power.  She also has the ability to create fake gems, which aren't as powerful as the originals, but give her the same abilities.

Her powers include telepathy with Washu and Ryo-Ohki, flying around, teleporting, phasing through solid objects, regenerate missing limbs, creating dopplegangers (a double of herself), telekinesis, creating forcefields, doing matter formation (manipulating matter and changing into that form.  Think of OVA Episode 6 when she morphed with the stone pillar), hair needles and creating energy swords and energy blasts.

She is very emotional.  She gets upset easily and she's short tempered, especially around Aeka.  But she's deeply in love with Tenchi, especially after episode 6 where he rescues her from Kagato.  While she was trapped in the cave, she was able to create an astral body (sort of like a ghostly consciousness) and venture outside the cave a short distance.  She watched Tenchi grow up over the years, and she wished more than anything to be with him.  However, the way she introduced himself to her was terribly frightening to Tenchi, so he distanced himself from her for a long time.

Ryoko has no tastebuds and only eats to be social.

Tenchi Universe

In this series, Ryoko is once again a space pirate, but she isn't a slave to anybody.  She was introduced to Tenchi by crashlanding into Earth during a firefight with Mihoshi.  Tenchi found her and it was almost love at first sight.

We have no idea who her parents are or her origins.  Those are never revealed to us.  Her physical age is 17 again, however, I have no idea if she's older than that.  No differences to age is ever mentioned in the series.

She can still summon an energy sword and shoot ki blasts, but she doesn't have any gems which would be the source of her power.  She can also fly around and teleport, but she can no longer summon demons.

Again, she's very emotional and brash, but not as much as in the OVA, and enjoys doing things to make Aeka mad, which includes flirting with Tenchi.

By the end of the series, she loves Tenchi to the point where she nearly dies for him.  Her love for Tenchi is downright obsessive.

She still maintains control over Ryo-Ohki, and that is her spaceship she uses to get around in outer space.

One more thing, she actually has tastebuds in this series as well as a need to eat or feed herself.

Tenchi in Tokyo

Once again, Ryoko is a space pirate in this series.  Her crime that she was in the process of running away with, is what brought her to Earth, was her stealing the Jurai Lightstone, which consequently brings everybody to Tenchi's planet all at once.  She pilots a pink Soja, which looks identical to OVA Kagato's ship, except it's PINK!

Her physical appearance is considerably different in comparison with the other series due to the artwork.   Her attitude is also very different.  She's more violent, and screams a lot more.  Many things get blown up around her.

Her obsession over Tenchi is still there, but that's basically the only characteristic that remains consistent throughout every series.

She still retains the ability to summon an energy sword and fire energy blasts, but Ryo-Ohki doesn't belong to her.

She falls in love with Tenchi after a major battle between her and everybody else.  Unfortunately, she was severely injured, but Tenchi remained by her bedside, taking care of her, and because nobody had done that for her before, it sparked her love for him there.

Pretty Sammy OVA

In this series, Ryoko is a normal school girl.  Not a very good student (becha didn't know that. :) ) and loves flirting with Tenchi.  She's still very strong and skilled in martial arts, but she has no powers at all.

She doesn't own/control Ryo-Ohki either.  She's just a normal person with Cyan hair who goes to school with Aeka, Sasami, and Tenchi.

Again, she gets into fights with Aeka constantly.

However, in this series, she doesn't make many appearances at all.  She's in the first episode and the last one, but she doesn't make an appearance at all in the second one.  She's not a main character.