Some movies have certainly moved me to tears. Music? Not usually intrinsically, but perhaps sometimes through an association with some personal memories. But some music can certainly fit and intensify my occasional melancholy mood. Examples:
Fairport Convention / Sandy Denny play "A Sailor's Life" off the CD Unhalfbricking
Fairport Convention / Sandy Denny play "Crazy Man Michael" off the CD Liege and Lief
Bella Hardy sings "Cruel Mother" aka "The Greenwood Side" on the CD In The Shadow Of Mountains
Cat Stevens sings "Sad Lisa" on the CD Tea For The Tillerman
Miki Howard covers "Strange Fruit" on the CD Miki Sings Billie
Emily Sangder sings "It Never Entered My Mind" from the 1940 Rodgers and Hart musical Higher And Higher
Carla Bruni sings ABBA's "The Winner Takes It All"
Bobby Goldsboro sings his big hit "Honey" live
Cassandra Wilson sings "I'll Be Seeing You" on her 2015 Billie Holiday tribute CD Coming Forth By Day
Bobby Gentry sings "Ode To Billie Joe" live on the BBC
https://www.youtube.com/watch?v=nv33eaygVDQ
Rebecca Ferguson covers "Don't Explain" on her 2015 Billie Holiday tribute CD Lady Sings The Blues
https://www.youtube.com/watch?v=yX5q24kZRRU
Jacqui Hamilton covers Janis Ian's "At Seventeen"
https://www.youtube.com/watch?v=PezdETwVSQY
Laura Fygi covers Don McLean's "Vincent (Starry Starry Night)" on her CD Jazz Love
https://www.youtube.com/watch?v=7pHRrX7LwlY
Barbra Streisand sings Johnny Mercer's "Autumn Leaves" which was based on Joseph Kosma's "Les Feuilles Mortes" (french), on her 1966 CD Je m'appelle Barbra.
https://www.youtube.com/watch?v=TiRvvorZ4ic
Elina Duni covers Leo Ferre's "Avec Le Temps" on her CD Baresha
https://www.youtube.com/watch?v=niKDugc9E7o
Soprano Anita Rachvelishvili has a new CD out, titled "Elegie", which includes some melancholy songs.