Let's start with the story: I'll try to keep it spoiler free.
Story: Light Yagami is a young, Japanese male genius who is bored with life. One day he finds something called a Death Note, a notebook with the ability to kill. He uses this death note to rule down on all he deams unworthy (criminals). He sets off his plan but a group of investigators and one main one set off to find this killer (Light) and that is the premise of the show. It carries through and is quite the thrilling anime with situation after situation stopping Light and him cunningly find a way around it. The series really starts to die down after episode 26 though with most of the corners being cut and everything coming down to "I'll just have to kill you before you kill me!" It still has a spark but it doesn't ignite as well.
Next is the art style.
Art: The design and art style of this anime is very unique. It takes a modern day gothic style but applies a civil, sharp manner to it. If something looks sharp enough to stab you, that'll say something about that character or object. It keeps it either very dark or very vibrant. It likes to mix the two up to make a beautiful painting that is Death Note. It'll stay unique and you'll remember how it looks.
The sound is critical so I'll talk about that.
Sound: As previously stated above, the show takes that Gothic theme into mind. Even the first set of opening and endings applies this style to the show. If something needs a dramatic, classical themed background song, it'll use it to it's best. Later on, the show picks ups a more chaotic feeling and even applies that through it's second opening and ending. Though I'm not a big fan of the second opening and ending, it does fit quite well.
The characters... Well...
Character Development: Personally, I didn't hate any of the characters. They all fit their roles in they were designed but I feel as if their attitudes were all copy paste. Each character looks different but the villains, excluding light, are all just in for the reputation, money, and power. All the detectives behind the Kira/Light case are justified and want to stop everything, though they may actually conflict with each other. Nothing just felt really special about any of the characters besides Light, L, Misa, Ryuk, Light's father, Near, and Mellow. Those were the only characters that stood out to me. Besides that, no one was too special.
My overall enjoyment/overall feeling of the show are about the same: It's a great anime that I suggest to everyone because it has it's own unique style and feeling towards it's audience but it really starts to lose what made it so great after episode 26. If you're going to watch it, stop after that episode. Leave everything else up to your imagination. I watched it because I wanted to see what was canon and I don't quite regret it but nothing popped out to me. It's great, exciting, but lack luster in the end.
