Tenchi Masaki, a trainee at his grandfather's shrine, was snooping around an ancient cave when he discovered and accidentally released a demon from it with an ancient sword. The demon turned out to be Ryoko, a spacepirate that had been sealed in the cavern. She decides to take out her anger at being imprisoned on Tenchi, but ends up being defeated again with the same sword. She disappears and Tenchi returns home, thinking the ordeal is over, only to find her in his bed. From this point it seems as if a never ending stream of alien women begin to arive at his home: Ayeka and Sasami, princesses of a distant planet called Jurai; Mihoshi, a blond airheaded member of the galaxy police and her more level-headed partner Kiyone (tv series only); and Washu, a galactic genius and scientist. And best of all, they all seem to be in love with Tenchi!
Tenchi Muyo began as an OVA series, and later spawned two tv series, Tenchi Universe and Tenchi in Tokyo. I believe there may also be a manga, but I am not sure. The stories in Tenchi Muyo and Tenchi Universe are drastically different, adn Tenchi in Tokyo is a continuation of Tenchi Universe. I (and most other true anime fans ^_~) prefer the OVA to the tv series, but all will be represented here ^_^.