Are there any songs that just turn you into a puddle of tears as soon as you hear them?

Yes!

9 Crimes - Damien Rice
Light - Sleeping At LastShe Will Be Loved - Maroon 5Burn - Ray LaMontagneTowers - Bon IverIf I Go, I’m Goin’ - Gregory Alan IsakovThe Trapeze Swinger - Iron and WineWires - Athlete Iris - The Goo Goo DollsThe Funeral - Band of HorsesWhere The Story Ends - The FrayWherever You Will Go - The CallingI Know It’s Over - The SmithsLover, You Should’ve Come Over - Jeff BuckleyWork Song - Hozier Trouble I’m In - TwinbedRun - Snow PatrolShooting Star - Air TrafficSamson - Regina SpektorHot Gates - Mumford and SonsHigh Hopes - KodalineMedicine - Daughter