VERY MILD PLOT SPOILERS. YOU HAVE BEEN WARNED.
Death Note is nearly a masterpiece; it certainly deserves to be one of the most popular anime of all time. The mystery and drama are played off incredibly, and the two MCs bounce off each other perfectly.
Light Yagami is a student who, one idle school day, sees a book fall from the sky. He learns that writing somebody's name in said book will cause them to die soon after, with more caveats and freedoms explained later in the show. The book's associated Shinigami, Ryuk, is entirely ambivalent towards Light, and couldn't care less whether he kills anyone or not. Of course, being a bored and borderline psychopathic student, Light starts murdering prisoners. The police catch onto the suspicious deaths and send their best detective, L, to figure out what's happening. Every time L gets closer to the truth, Light is one step ahead, having prepared for it nigh perfectly. The intelligence of both characters is probably my favourite part of the show. Their personalities play off each other brilliantly, and their plans both make sense and are amazingly well thought out. It was a blast watching each of them make a leap forward, only for the other to make two immediately afterwards. It stays interesting with very few low points. Light and L interact on many occasions, with L even asking Light directly whether he is the murderer. Of course, Light pretends to be innocent by feigning ignorance, but L still suspects him. This part is outstanding, since neither character has the abject advantage, and both are struggling against the other. The other side characters aren't worth mentioning due to spoilers, but suffice to say they're uninteresting yet play a vital part in the plot development.
The book, or Death Note, is more complicated than simply a book as expected, but thankfully there are no plotholes - it stays self-consistent and entertaining. There are more Death Notes in existence, and this comes into play partway into the show in a brilliant way. Light comes up with several plans regarding them, including recruiting other people to help him survive.
Whether Light is a protagonist or an antagonist is debatable. He wants to fix the world by killing criminals, but by doing so he is a mass murderer. This moral quandry is extremely captivating since you never know if Light is going to win or not; it is kept ambiguous until the very last episode, where it ends satisfyingly. I cannot say whether he wins or loses, since that's part of the fun, but the ending is done well.
The worst part of the show is when a new detective, Near, is brought on the scene to deal with Light. It starts to get boring - Near is smart almost beyond comprehension. It always seems like he knows exactly what's going to happen, but not in an interesting way like L did. The battle of intelligence devolves into a constant exchange of "no u". Near is uninteresting, to say the least. He's basically a stripped-down version of L, and I have no idea why he was introduced as a character other than to serve as Light's enemy. Still, Light remains smart and manages to evade Near in some ingenious ways.
To wrap up, Death Note is an outstanding anime with one relatively minor flaw. If you're at all into anime, this is a must-watch. I thoroughly enjoyed my time with it. It's a little heavy on the brain, but of course that's part of its appeal. A solid 9/10.