3 x 3 Eyes

Elfen Lied is bigger and better, it features lots of blood and a very similar main character. With both animation and story a grade higher then 3x3 eyes, but the same basics, i don't see any reason you won't like it.

Very similar animes in several respects. Lead female (Powerful, non-human characters in each) have two personalities. One overly cute, the other serious or even evil. Their lives become entwined with those of an ordinary lead male and an ackward relationship develops. Both contain a quite a bit of blood. Animation style is one of the biggest differences. If you enjoyed the plot or character relations of one, I'd definitely recommend watching the other.

Pai also has a split personality, like Nyu, vascillating from innocent know-nothing to a cold-blooded serial killer.  The effect is quite chilling in both anime.

In both Elfen Lied and 3x3 Eyes, an ordinary male protagonist is shoved into abnormal circumstances and thus tied into the life of an unusual girl with two personalities. There wouldn't be any story if love didn't sprout from this, nor the occasional humor, but the gore and violence definitely makes these not lighthearted. They both share a similar feel and are both excellent; you can not go wrong with either of these if you like this type of show. Though 3 x 3 Eyes doesn't have the ecchi qualities of Elfen Lied and has more horror elements.

The overall mood in each of these anime is dissimilar, but they share lead female characters that go from dangerous, and even evil, to sweet and completely innocent in a heartbeat. Both series are violent, Elfen Lied being much more so. Both anime develop a romantic relationship involving an ordinary boy and an extraordinary girl. 3x3 Eyes has a supernatural element that is absent in Elfen Lied's more realistic setting. The split personality of the main characters, and the problems they cause is the main reason to justify this recommendation.

Both 3x3 Eyes and Elfen Lied have a main female character with a double personality; she is either a cute and innocent teenager or a deadly and powerful creature who seeks to have a normal human life.

3 x 3 Eyes explores the innocent yet very powerful Pai in the same way that Elfen Lied does with Lucy. Both Lucy and Pai have two personalities, one being cute and innocent and the other being very powerful and ruthless.

Both leads have 2 very different personalities. One is a pretty clueless fun loving girl. The other kills without remorse. Both anime have a lot of bloodshed. 3x3 eyes doesn't have any of the ecchiness that Elfen Lied does. If you liked one check out the other.

Both 3x3 Eyes and Bastard! are short OVAs where gore is the main theme. In 3x3 Eyes a magical race is the main feature while in Bastard! it's a wizard. Definitely very comparable series!

Powerful being trapped in human bodies, Parvati IV from 3x3 Eyes and Dark Schneider from Bastard!! have some immediate similarities. Watch out when they break free, as charnage soon follows. Both short OVAs with plenty of action, if you enjoyed one, you should check out the other.

I had no idea the same creator had made 3y3 Eyes and Blue Seed till way into the series, so keep in mind I didn't make this recommendation for that reason. They both have an alarmingly similar feel to them, with plenty of horror and monsters to go around. I admittedly enjoyed 3x3 much, much more... but if you liked one, you'd appreciate the feel of the other.

I believe the person who wrote the manga for Sazan Eyes and Blue Seed is the same.  Both anime involve a young protagonist who encounters a mythical element/power/figure;  They are then entrusted to use their newly found power to fight the forces of evil