One of the songs, simply referred to as 'Anticipation' (Kitai), is unlike any of the other tracks. It's a smooth electronic theme with a dark undertone - a perfect theme for a present-day noir story, which essentially is what Death Note is.
Also, Death Note Theme is just as awesome, maybe even more. By the way, this is a fragment of Dies Irae, and this hymn also inspired many other great pieces of music, including Mozart's Requiem. The few times we hear it in its entirety in the anime, it's always chilling. The most memorable is when Higuchi is finally put into a corner, and you realize that he's utterly fucked. It starts off with the Ominous Latin Chanting as the police blockade the highway, gets a bit more intense when it's revealed that Aizawa and Ide organized it without L's orders, reaches the peak of its crescendo when L turns the spotlight from his helicopter on Higuchi, and ends with Higuchi spinning out and ending up with his back against a literal wall.
L's Theme B. Yes, L has multiple themes. This one adds a somewhat playful spin to the original "Tubular Bells" Expy that he had before. And then someone called Eshmasesh went and remixed it into something even more awesome.
For a series that relies heavily on old-style rock/slow rock and epic Latin chanting, there is still a hidden gem that could only be described as sunset, calmness, and love.
Near's Theme and Mello's Theme are simply brilliant, like L's. A little bonus Awesome: play Near's Theme and L's first theme at the same time. The themes compliment each other well and seem to echo at times, the way L and Near echo each other. Near's theme uses more "modern"-sounding instruments than L's; a very synthetic keyboard instead of classical piano, much more overdriven guitar, etc. This, combined with the similar structure and melody, helps create the feeling that Near isn't just similar to L he's the next generation of the same character. Moreover, L's Theme contains two sections repeating, each with a distinct time signature and orchestration. The first uses a very unusual 7/8 time signature and a piano piece, while the second uses the more common 3/4 time signature and a rousing electric guitar beat. Near's theme exclusively uses the 7/8 section, contrasting to the 3/4 signature of Mello's theme. A nice way to represent the two sides of L: the cold, rational side and the ambitious, emotional side.
Requiem is not a happy piece, but it is gorgeous, and the lyrics and harmonies and language and everything just encapsulate the scene so perfectly.
The two openingthemes are all kinds of awesome, especially the second one. What's Up People! is quite likely the most metal and hardcore anime opening to date. With its opening whispers it turns into a roar of power that would rip the ears off of anyone expecting a radio friendly j-pop song. It then proceeds to laugh mercilessly as it bleeds them out culminating with a series of frantic screams that leave you grasping for air. Maximum the Hormone somehow managed to make Death Note more badass. That deserves a fucking medal.
Though somepeople seem to find the first one just as, if not even more, epic. The endings to each season reflect Light Yagami's state of mind at that point in the series. The first emphasizes Light's descent into darkness. The second is about the ascension of Kira to God, as well as foreshadowing his eventual downfall.
"God Is Watching You", especially in the scene it appears in. (The Japanese version is quite good as well)
Then there's Light's Performance. Take his original theme, reduce it to base elements, grow it up and darken it, layering the same base melody over itself again and again and again and ... It's so simple, but becomes increasingly complex as it goes, and it's ominous and cold and wonderful.
All of the theme songs for L, Mello, Near, and even Mikami. They only play when a blow is being struck against Kira, whether or not any of the characters realize it at the time. Think about it. L's is played when he's first introduced, a blow against Kira. Near and Mello's, and again, even Mikami's introductions led to Kira's eventual downfall. And then, every time you hear their music, they're doing something that could potentially catch Kira. Even though Mikami was Kira's proxy, and even God's Right Hand, his introduction was so public that Near was able to take advantage of him, and besides he was the catalyst that brought Kira down.
Kyrie 2. It's the first thing you hear in Death Note, and it perfectly sets the tone of the world as it is before the events of the series begin, in the rotting worlds of the shinigami and humans.
Hesitation, one of the lesser known soundtracks, is written quite cleverly. If you listen to it, there are constant rhythms which just repeat over and over again, which adds suspense. Also, it sounds a bit like a clock ticking, like you're waiting for something - hence the name Hesitation. The moments where it builds up to something then drops back to normal are also really good at sticking to the name, because it's like you're about to do something, but you hesitate and the opportunity is gone. It's pretty clever.
The musical's heart-stopping Overture. A single name four times and a diminished chord are all it takes to show the audience exactly the kind of story that's about to come.
Kira! Kira! Kira! KIRA!
"Only Human", a duet between Rem and Ryuk, singing about how pathetic they think humanity is.
"Playing His Game", a duet between L and Light, is pretty awesome, too. Especially if you're a Lawlight shipper.
"When Love Comes", Rem's song. It doesn't even sound like it would be from a Death Note musical, but instead the credits of a movie.
"Hurricane", an early act 1 song in which Light makes the decision to use the Death Note to cleanse the world. It perfectly captures Light's thoughts from shock to resolve and a desire to bring retribution to create a better world. And a karaoke version exists!