 If you liked
Monster
|
 ...then you might like
Kyougoku Natsuhiko: Kousetsu Hyaku Monogatari
|
Both anime have the same composer (Kuniaki Haishima), both series have creepy theme songs, and both have Karen Strassman in the cast.
To a deeper extent, both anime deal with self-discovery and they venture into the more philosophical ideas of life. Both Monster and Requiem are dark, deep series with few moments dedicated to humor. There's a huge element of mystery in both series and, in the end, you'll enjoy Requiem from the Darkness if you liked Monster.