Ok, there's lots of spin-offs of this show, so let me say right now that the OAV series is the best! This is the one where Tenchi wakens the demon ~Ryouko~, and things go downhill for Tenchi from there. The TV series does have some really funny episodes ~Time Travel and Space springs to mind~ but as for storylink, the OAV series has the best written and the most interesting of all of them. Plus Kagato is the coolest enemy!
Tenchi Muyo: No Need for Tenchi*
Here you can order your very own copies!