If it's not obvious enough, this contains spoilers.
The story of Elfen Lied is a sad one. Though I liked the story, I found that much was left out in the 13 episodes. The pace was a good pace, slow at times, fast at others, and they really did jam as much as possible into each episode. I feel as though more could have been explained, the Diclonius disease was a bit of an enigma.
I also want to know who was at the gate at the end of episode 13, they really could have continued the series. The implication of Lucy's death wasn't really enough for me, I wish they had shown more of it, as it would provide more closure in the storyline. And what of Kouta and Yuka's romance? I want to know more about that!
The characters in Elfen Lied mostly have sad backgrounds. For the most part, they are happy people, but I didn't really like how all of them had such tragic back stories. Yuka was the only character I didn't like and she didn't have a sad story. I feel like Lucy and Nyu should have been integrated at the end, I didn't like Nyu, but I did like Lucy. Kouta was an aazing character, his personality was perfect for his backstory, and the whole center of his personality changed when his memory came back.
I personally wanted Lucy and Kouta to be together, Nyu to just go away (or integrate with Lucy), and Yuka to deal with the fact that she doesn't get to be with her cousin.
As for Mayu and Nana, they were both likable characters. Mayu was a generous girl, who's story freaked me out, but she was always friendly and likable to me. Nana I think was a little over the top about finding Lucy, but it makes sense seeing as the girl got her limbs chopped off by Lucy.
Bando was someone I really hated, I mean, one second he's saying, 'if anyone's giving you trouble, give me a call and I'll kill 'em for you' the next he's about to knock Mayu out.
Although I didn't leave a rating for this section, I loved the intro song, Lilium, and how they had it in the story.
Overall this was an anime that grabbed my heart out of my chest, slammed it into the ground repeatedly, and then put it back and brought it back to life, only to crush it in the end. But I loved it just the same, and thought it was wonderfully bloody.