Ryoko is a space pirate, hundreds of years old and wanted throughout the galaxy. She acts as the catalyst for most everything weird or bad that happens to Tenchi. In the OAV, she was sealed in a cave near the Masaki Shrine by Yosho 900 years ago, and it was Tenchi's curiosity (and stupidity, some may say) that allowed her to escape. However, in the TV series, she was being pursued by Mihoshi, who actually thought she stood a chance (yeah, right...). Ryoko unwittingly caused her greatest rival, Ayeka, so she's also indirectly the cause of all the catfights (and most of the property damage) in the Tenchiverse.
Ryoko is absolutely obsessed with Tenchi and is always plotting ways to win him over, get him in bed with her, take a bath with him, etc. This usually infuriates Ayeka, causing the aforementioned destruction (both Ryoko and Ayeka can manipulate powerful energy).
In the Tenchi Muyo! OAV series, Ryoko was created by Washu, but is controlled several times by Kagato. Ryoko, under Kagato's power, attacked Planet Jurai 900 years ago and was driven away by Yosho and sealed in the cave on Earth. Her three Power Gems were taken away and selaed in the Tenchi Sword (see Tenchi's page for more info on the Tenchi Sword). Ryoko can use her gems to summon demons, fire energy bolts, fly, or call upon her spaceship/pet, Ryo-Ohki, and it is said that if she had all three gems, she would be the most powerful being in the universe. Unfortunetly, in the TV series, Ryoko has a much less colorful background and appears to simply be a space pirate with a lot of power... She is, however, chased by the bounty hunter Nagi and her spaceship/pet, Ken-Ohki.