...and another one of my favorite songs:

Clint Mansell - Lux Aeterna

btw, this song was later remixed into the trailer for the LOTR - 2 towers, not the other way around: wikipedia

Requiem for a Dream (soundtrack) (wikipedia)
Requiem for a dream (movie) (wikipedia)
Requiem for a dream (movie) (imdb)

Clint Mansell - Lux Aeterna (Paul Oakenfold remix)

Animatrix - Lux Aeterna