It's a nameless song made especially for the show by a band called "The Crystal Method."
Sea Lion by Sage Francis
The song played when Bones was listening the tapes: When I fall by Lizz Wright The song played while Bones was preparing dinner: Oh Darling by Happiness
Song played.. Obsession by Animotion.
Pharrell - Despicable Me
Its Desensitize by Karl Wolf
Click the related link for information about the song.
The National Anthem.
Wiley - Morgue
The song played at the beginning of "Farrah's Story" is Queen of the Slipstream by Van Morrison.
Nobody remade it for The Watchmen, it's another song by Smashing Pumpkins. They have "The Beginning Is The End Is The Beginning" and "The End Is The Beginning Is The End." The song played in The Watchmen trailer was "The Beginning Is The End Is The Beginning."
The song played at the beginning of the show is not titled "Bless the Beauty and the Children." If you provide the name of the show or more context, I could help identify the correct song.
The song that plays at the beginning of Twilight is Full Moon by the Black Ghosts.