This is a rewrite of an old review I did, because let's face it, I though it wasn't very good.
Elfen Lied is one of the more interesting anime I've come across. The story is about a mutant race called the Diclonius, who have been discriminated by humans, and have been locked up in a secret government facility. The Diclonius have 'vectors'; telekinetic arms that have the power to cut anything in their path. Their deadly DNA, however, has been known to cause the Diclonius to kill humans and infect human males with a virus that makes their children Diclonius themselves. One of the test subjects at the facility, a girl known by the staff as 'Lucy', escapes, and goes on a murderous rampage, but is cut short when a bullet injures her in the head, knocking her unconscious into the sea...
The best thing I thought about the anime was its soundtrack. I'll admit it right now, if I didn't hear it's opening theme, 'Lilium', I probably wouldn't have gotten interested in Elfen Lied in the first place. It's a lovely mix of happy J-Pop and sad, sombre orchestral pieces. Then again, I don't really think the J-Pop ending fits the overall tone of the show. (But if you read the lyrics...).
The characters do act pretty... well, stupid sometimes. Yes Kouta, take the naked, horned girl home and not call the police! Also, you may be divided on whether Lucy was really justified in killing many people. You'd think that Lucy would have a bigger reason than just the fact that she had a crap childhood filled with torments from bullies. Then again, that's pretty terrible in itself.
The art style is (in my opinion), bland moe, but the backgrounds are beautiful. The animation also flows decently.
The worst aspect of Elfen Lied has to be the pointless fanservice. Seriously, I want to learn more about the characters, not see Nyuu run around naked! Also, since the anime started before the original manga it was based off finished, many characters and plot elements were cut from the anime (especially towards the ending) and thus, it can get confusing.
Overall, it's still a marmite anime - you'll either love it or hate it. Be warned though, the series is infamous for its graphic violence and nudity, so if you're sqeamish, give this a miss. If you think you can handle it, give this a go! It's only 14 episodes long, including a OVA.