OK, now that I have gotten that off my mind, I'll introduce you to the Tenchi Muyo! sagas.  All three that I know about are different stories of the same teenager, Tenchi Masaki.  Tenchi is a high school student living in the countryside of Japan.  His father is a widower and and architect, and his grandfather is the keeper of the family's Shinto shrine.

 

In the beginning of the first saga (Tenchi Muyo!), Tenchi comes face to face with a space pirate who his ancestor sealed away in a cave 700 years ago.  Then, Ayeka, the crown princess of Jurai (another planet in a far-off galaxy) and her little sister Sasami show up and kidnap Tenchi and the pirate, Ryoko.  Ayeka's ship crashes on Earth, and the three aliens are stuck on Planet Earth.  Unfortunately, Ayeka and Ryoko start fighting each other for Tenchi's love.

 

In some pretty weird and downright impossible unexpected twists, Washu, a science academy graduate and mad scientist and Mihoshi, a Galaxy Police reject end up staying at the Masaki home.

 

The next saga is the silly, stupid, and outrageous Tenchi Universe.  I don't really know much about it because I found it too stupid for my tastes.  All of the titles start with "No Need For..." and then something like carnival ("No Need for Carnival" was actually a good episode) or bounty hunters or whatever.

 

Now for the one saga I like best:  Tenchi in Tokyo.  The animation is just a little bit different, but the entire saga is worth it's weight in platinum.  Tenchi goes to school in Tokyo, leaving the girls and his family behind.  While there, he falls for the popular girl, Sakuya Kumashiro, and she falls for him.  Ayeka and the others are extremely pissed off, thinking they are more deserving of Tenchi than this girl Sakuya.  Washu creates a device that transfers someone from a given location to wherever they want to go.  After several invasions, Tenchi asks Washu to take the device down and turn it off.

 

Someone, a little girl with psychic powers named Yugi is behind the eventual separation of the Masaki family (to which the girls belong).  She wants to take over Earth, and she has to break up the bond that holds everyone together.  Her shadow is none other than Sakuya, who doesn't even exist.

 

I hope that this gets you to find the series/sagas on VHS/DVD volumes so you can watch the three versions of this series.  It's good, and nothing else can compare.