I have seen that the reviewer "Sebkedos" mentions "If you like Evangelion, you'll have fun with Elfen Lied". Well, Mr. Seb, you are right.
Elfen Lied is the most brutal, violent, sick, twisted, bloody and gory anime ever. And I loved it. Parents, get the away from this one if you want sanitized entertainment. It has everything to corrupt the youth (nudity, gore, extreme graphic and psychological violence).
The story is about as straightforward as anything. Diclonius are mutants who possess "vectors" (invisible hands) and have the power to exterminate humanity. Trouble begins when one such diclonius, named Lucy, escapes from the research facility off Kamakura (and we are treated to a gruesome scene in which she disembowels and kills 23 guards). The rest of the series is about how the research people, the Special Armed Forces and the police try to retrieve the diclonius, and fail - but they set the stage for a lot of bloodshed.
Straightforward? Yeah, I thought so. However, it is like NGE: it has its share of hidden meanings. It treats subjects such as human psychology or the nature of violence either directly, or through allegories. It has its characters with tragic back-stories, and the use of flashbacks to reveal these. It also looks into the minds of characters, who have their own emotional and psychological problems (example: Lucy/Nyu suffers from split personality disorder) This also goes for its stunningly realistic artwork; I'm talking especially about its backgrounds (they remind me of old paintings somehow).
Trivia fact: in the intro and the outro, paintings by Gustav Klimt are reproduced (ofcourse, using characters from the series).
Overall, one of the best series I've ever seen. Highly recommended for fans of psychological or progressive anime.
Advice: stay away from the OVA. It takes place between episodes 10 and 11, adds nothing to the story and to add insult to injury, has COMEDIC undertones! What the bloody hell is with the comic parts in the OVA, whereas the series has an unmistakeably serious tone, I don't know. This has annoyed me.