There are sad songs. There have always been sad songs. Sad songs are good songs, we like listening to them because either we're sad ourselves, or we have been. Listen to a sad song when you're happy, and you feel a pang of sympathy (sometimes followed with a grudging sense of the singer ruining your fun). Listen to a sad song when you're sad, and you don't feel so alone. If I were more classically inclined or more of a douche-bag, I'd have a big section here on tragedy and catharsis and Nietzsche and everything, but I'm not. I'm just a big enough douche-bag to tell you that there's an entire book of the Bible dedicated to sad songs, the Lamentations of Jeremiah, and that settings of the O Vos Omnes (Oh, all you who pass by, stop and listen, see if there is any sorrow like my sorrow) were especially popular in the Renaissance.
I like sad songs. When I'm happy, sad songs elicit a pang of sympathy. When I'm sad, sad songs are sort of comforting. Everyone, secretly, has one sad song that they love.
I have many.