Before the age of internet downloads, cable tv was just starting, and dvd's - the only way a person could have enjoyed anime was to go to stores like FYE (Camelot and Suncoast at the time) and Bestbuy and load up on overpriced VHS tapes - but there was some lights to the fledgling American Anime fans - these were Robotech, Star Blazers, Voltron, Sailor Moon (sorry but it is true), and TENCHI.
Poor Tenchi - he is a 16 year old earthling who lives with his father and grandfater who is a priest at a local shrine but his world is about to take a complete 180 when a spaceship lands in the lake that he is standing at and sees a cute, but drunk lady. When she comes to, she says she is Ryoko, and an evil space pirate is pursuing her - then a giant suit of combat armor appears and attacks. Soon the "pirate" is discovered to be everyones favorite ditzy detective Mihoshi and Ryoko is the evil space pirate. This starts the story, and as Tenchi puts it the carnival that his life will take as other girls come into his life, the princesses Ayeka and Sasami, the mad scientist Washu (who is a genius, but things tend to blow up in her face), Kyone the GXP detective who has to put up with Mihoshi, and others who pop in and out. But Tenchi has a destiny, and these girls are the key that will take him to other dimensions, and into space.
I first got into Tenchi by seeing the first movie (which actually takes place in this universe not the OVA's). You can say he is the start to the harem comedy series that all others copy from. A definate classic that anyone can enjoy with laughs, cringes and head shakes. Enjoy!