Obviously there is no such thing as a 'sad song', but everyone likes lists:
http://www.pastemagazine.com/blogs/lists/2015/05/the-50-saddest-songs-of-all-time.html?a=1

1. Sufjan Stevens – “Casimir Pulaski Day”
2. Hank Williams – “I’m So Lonesome I Could Cry”
3. Johnny Cash – “Hurt”
4. The Magnetic Fields – “I Don’t Believe In The Sun”
5. Dolly Parton – “Jolene”
6. George Jones – “He Stopped Loving Her Today”
7. Jeff Buckley – “Hallelujah”
8. R.E.M. – “Everybody Hurts”
9. Etta James – “All I Could Do Was Cry”
10. Roy Orbison – “Crying”
11. Harry Chapin – “Cat’s In The Cradle”
12. Aretha Franklin – “Ain’t No Way”
13. Joy Division – “Love Will Tear Us Apart”
14. The Velvet Underground – “Pale Blue Eyes”
15. Johnny Cash – “Long Black Veil”
16. Vern Gosdin – “Chiseled in Stone”
17. Gary Jules – “Mad World”
18. Beck – “Lost Cause”
19. Drive-By Truckers – “Little Bonnie”
20. Laura Viers – “Sadako Folding Cranes”
21. Neutral Milk Hotel – “Two Headed Boy Pt. 2”
22. Amy Winehouse – “Back to Black”
23. Townes Van Zandt – “Waiting Around to Die”
24. Camper Van Beethoven – “All Her Favorite Fruit”
25. Bruce Springsteen – “The River”
26. Glen Campbell – “I’m Not Gonna Miss You”
27. Sarah McLachlan – “When She Loved Me”
28. Justin Townes Earle – “Yuma”
29. Sinead O’Conner – “Nothing Compares 2 U”
30. Pearl Jam – “Last Kiss”
31. The Mountain Goats – “No Children”
32. The Louvin Brothers – “The Angels Rejoiced Last Night”
33. Patty Griffin – “Making Pies”
34. Elliott Smith – “Fond Farewell”
35. The Smiths – “There Is a Light That Never Goes Out”
36. Tom Waits – “Anywhere I Lay My Head”
37. Sun Kil Moon – “Carissa”
38. The Postal Service – “The District Sleeps Alone Tonight”
39. Robyn – “Dancing on My Own”
40. XTC – “Dying”
41. Brad Paisley and Alison Krauss – “Whiskey Lullaby”
42. Iron & Wine – “The Trapeze Swinger”
43. Ben Folds Five – “Brick”
44. Eric Clapton – “Tears in Heaven”
45. Perfume Genius – “Mr. Peterson”
46. Vic Chesnutt – “Flirted With You All My Life”
47. Shelby Lynne – “Heaven’s Only Days Down the Road”
48. Delta Spirit – “Vivian”
49. Tammy Wynette – “D-I-V-O-R-C-E”
50. Angel Olsen – “Windows”