I add
Please save my Earth (Boku no Chikyuu wo mamotte)
The anime is nice and well done, but if you want to know the whole story you need to read the manga.
also
The twelve kingdom (Juuni Kokuki)
and
Magic Knight Rayearth
Furthermore I don't know how much you are into very very old classic but
Versailles no Bara
Is one of the most influential and known shoujo of all time. I recommend it even in spite of its age.
There's also
Utena which was extremely popular on its time, I've been watching it for the past few days and I almost finished it, but I have really mixed feelings about it. There are elements of pure genius mixed into sloppy and repetitive storytelling, bad animation, and retarded comedy.