The first opening theme of Death Note, "The World" by Nightmare, has got to be one of my most favorite anime opening/closing themes of all time. And it's not just the song itself that I love, - it's the whole combination of the song, the animation sequence, and the total hotness of Light Yagami. Hehe... Watch it and see what I mean. :)
Videos and lyrics to this song as well as to the other opening and closing themes of Death Note may be found here:
Death Note Opening & Closing Themes