I enjoy sad songs as long as I like the music. There is something soothing about them. Even sad songs that are really angry give me a sense of peace. Is that "normal"?

There isn't one specific song but I will keep it short.

A Forest, Plainsong, Disintegration, The Same Deep Water as You, Out of this World, lots more - The Cure

Somewhat Damaged, The day the world went away, Right Where it Belongs, The Great Below, Hurt, Something I can never have, well most every song Trent has written falls in the sad song category - Nine Inch Nails

Losing my Religion, Perfect Circle - REM

Blasphemous Rumors - Depeche Mode

How Will I Laugh Tomorrow, Love vs Loneliness, Nobody Hears, Alone - Suicidal Tendencies

Everything from Joy Division