I'm probably from a different generation from the rest of you on this thread but a real weepy for me is Otis Redding's I've been Loving you too Long. One of the best love songs ever for me and brings back memories of a certain relationship.
Another which brings a lump to my throat for very different reasons is Sam Cook's A Change is Gonna Come - which is a kind of anthem of hope for the civil rights movement.
And Edith Piaf's Je ne regrette rien is one of the most powerful passionate songs ever.
But there are many more. Music can certainly make me feel emotional.