Well I have to say I'm disappointed about the posts on here regarding the Ryoko and Ayeka realationship.
Many people seem to be homophobic and close-minded. Everyone is saying that Ryoko and Ayeka hate each other, which is not true. If it were they did, they would not bother to help each other in the series.
I seem to see alot of people questioning if Ryoko and Ayeka are in love.
The answer is yes.
Just because they both care about Tenchi, doesn't mean they don't care about each other.
Sure they fight sometimes but it's like play fighting and they never seriously hurt each other. One could even question whether or not they hit on Tenchi just to get a reaction or attention out of one another.
Aside from just the Tenchi Universe episode "Time and Space Adventures Part 2" where Pretty Sammy shoots, what I like to call a 'truth' arrow, at them. There are many other incidents that show they care for each other.
In the series when Ayeka and Ryoko are batheing together they always blush. Ryoko will sometimes jump on Ayeka and give her a hug, and not to mention the times when she rips off Ayeka's towel.
If you watch the Tenchi series you will see quite a few moments of Ryoko and Ayeka bonding. (Cute actually.)
In the Tenchi Muyo Video Game (only sold in Japan) "Mimiri Onsen". They kiss and embrace without any outside influence from Pretty Sammy. http://www.youtube.com/watch?v=TkE8yG4OSsU
More info on the Tenchi Muyo "Mimiri Onsen" Video Game here. http://www.geocities.com/punistation/
Oh and if anyone actually buys and reads the Tenchi Muyo Manga. Ryoko and Ayeka actually confess love in them.
A nice Music Ryoko X Ayeka Music Video containing most of the Ryoko and Ayeka bonding moments http://www.youtube.com/watch?v=Z11XA-5vsWI