Elfen Lied, the first to be babbled about. 
Elfen Lied is probably known best for its abundance in nudity and gore (your parents are likely to have a problem with this). This anime is also a very sad one, so if you don't like gore or tragedy, don't watch it. However, I don't think people should avoid watching Elfen Lied due to the nudity, since most of the nudity in the show is sorta necessary and isn't of a sexual nature.
Plot Summary: The first episode is one of the best first episodes of an anime that I've ever seen. In the first episode, the viewer is introduced to the main character, Lucy, as she easily rips apart guards at a research facility naked. Lucy is a member of a new human race called diclonius; dicloni have horns (that look like cat ears) coming out of their skulls, have pink hair, and have extra, long, invisible arms called vectors. The anime follows Lucy as she's pursued by the facility researchers. However, in the beginning she is shot in the head and develops another personality named Nyu. Nyu is the opposite of Lucy (who is a bloodthirsty killer with a sad past) and she ends up living with 2 college kids, Yuka and Kouta. Kouta and Lucy have history, which unravels throughout the series whilst Lucy is being hunted. In total the series is 14 episodes long (13 episodes + and OVA episode that fits in near the end of the series).
Plot/General:
There are a variety of genres that pop up in Elfen Lied, such as comedy, tragedy, romance, and horror. The comedy consists mostly of hand jokes and the scenes with Nyu. The romance is a love triangle between Lucy, Kouta, and Yuka, but the series isn't really centred around this relationship. And of course, the horror consists of the abundance in severed limbs, halving, decapitating, and Lucy's mental instability.
The tragedy is the best part of the show though. Elfen Lied looks at the darker side of human nature, which includes murder, betrayal, torture, rape, and the blatant disregard of others' feelings. Humans regard dicloni as dangerous killer mutants, so all dicloni are taken from their parents or killed at birth. The dicloni who are taken from their parents are put in the research facility and undergo horrible experiments, despite the fact dicloni are just like humans in terms of personality a morality. So as Lucy's tragic past is revealed, the hardships of the other dicloni are revealed as well.
Unfortunately, the anime had to be cut short and couldn't follow through with the manga. The conflict of Lucy versus the researchers (mostly Director Kakuzawa) started out great in the anime, but the conflict died in the last episode without any good reason. If you're looking for a kinda suspenseful and intriguing plot, I'd suggest reading the manga; but if you're just looking for some easy entertainment with fantastic tragedy, then Elfen Lied is for you!
Art:
The art in Elfen Lied isn't very good. It's very similar to the art in most mainstream animes, since it's rather simple, doesn't have a lot of details, and slips up at times. However, the background art and character designs are pretty great. I actually prefer some of the anime's character designs over the character designs in the manga. The best art in Elfen Lied is found in the opening though; the opening's art is done in this cool style and it's really unique compared to most animes. ^.^
Characters:
Since the series is only 14 episodes long, there's a small cast, so almost everyone is featured in this list here... The dubbing is sorta half decent, since half of the characters are dubbed really well, but the other half have pathetic dubbing. In terms of the emotion given off by the characters, I think the dubbed version is way better, but that might just be a personal preference there. ^.^;
Lucy: I love Lucy's English voice. It sounds perfect for her character and it sounds so nice that you could listen to it all day (her Japanese voice sounds kinda average). She's the original (queen) diclonius who spreads the vector virus that causes people's children to be born dicloni (silpelits). All her life she's been discriminated for being a diclonius, and this has caused her to live a sad and lonely life that's full of regret.
Nyu/Nyuu: Lucy's other personality. She's sorta like Chii from Chobits; she says one word, "Nyu", and she's a complete idiot. I find her kinda annoying, but most people thinks she's cute. She serves as comic relief most of the time, which is kinda nice since most of the series is gory and depressing.
Kouta/Kohta: A college kid who takes in Nyu, not remembering that he's met her before. He's also very stupid and weak, but he takes in Nyu, Nana, Mayu, and Wanta, so he's kinda vital for the plot.
Yuka: Kouta's cousin who has been infatuated with Kouta since they were kids. She's actually a million times more annoying than Nyu, since she's always whining about not getting enough attention from Kouta and such. She lives with Kouta and the other characters in the Maple Inn.
Nana: A silpelit who helps hunt down Lucy, since dicloni can sense each other. She's nice and doesn't kill anyone. Also, she's loyal to Chief Kurama, so the researchers aren't very afraid of her and have performed many cruel experiments on her. She ends up being taken in by Kouta as well.
Mayu: A runaway 13 year old girl who was raped multiple times by her stepfather while her jealous mother did nothing to stop it. She's Nana's best friend, and lives in the Maple Inn with her.
Mariko: Another silpelit sent to hunt down Lucy. Her vectors are longer than Lucy's and she has more vectors than Lucy. She's been isolated in a dark room all her life. She's about 5 years old and is a bit of a psycho killer. She's another lucky character to get really good English and Japanese voice actors.
Chief Kurama: Second in command at the diclonius research facility. Nana calls him "Papa", but Mariko is his biological daughter. Lucy is trying to ruin his life partly for ruining her own. He has a great English voice actor who put the perfect amount of emotion into his voice, so he doesn't sound like a boring scientist guy.
Bando/Bandou: My favourite character! ^.^ He's a total asshole. He's the most "capable" member of the SAT team that's sent to kill Lucy, and he's even more bloodthirsty than Lucy. His character also has a brilliant voice actor.
Shirakawa: Kurama's fellow scientist lady. She cares about Kurama's well-being and helps advance the plot in certain points.
Director Kakuzawa: The head of the diclonius research facility. He doesn't care about anyone other than himself and his goals. It's unknown what happens to him in the end of the series. He's the top bad guy, the boss.
Arakawa: A research assistant who worked with Kakuzawa's son at the local university. She runs into Kouta at a bad time, and ends up being imprisoned by Director Kakuzawa. She doesn't get to shower at all. She's kinda funny too.
Number 03: A silpelit from the past who infected Kurama with the vector virus. Many harsh experiments were performed on her without mercy from the scientists, but Kurama showed some pity for her.
Sound/Music:
The opening theme, Lillium, is the main theme for the whole show. It's a gorgeous song and it's many variations are almost just as good. The other background music in the show doesn't catch the viewer's attention though. Also, the ending theme, Be Your Girl, is very annoying and doesn't suit the general mood of the series. However, the sound effects for the people being cut in half and dismembered are (disturbingly) realistic!
Overall Rating:
If you just wanna watch something 'cause you're bored= 4/5 
If you're looking for an amazing anime= 3/5
^ Bando making a funny face. XD
