As is usually the case, this is a thin category. Songwriting for film just isn't in vogue nowadays, but if you look close enough you can usually spot at least three of four decent Original Songs a year:
"Lay Your Head Down" from Albert Nobbs (Brian Byrne, Glenn Close):
This lovely Irish lullaby that concludes the film appropriately captures the film's subdued, delicate nature. Only used for the credits, but it's just so pretty.
"Star Spangled Man" from Captain America (Alan Menken, David Zippel):
One of my favourite moments of the film was the snappy montage set to this jaunty anthem that gently satirizes wartime propaganda in the spirit of a USO show.
"Lily (Rita)" from Chico & Rita (Bebo Valdes):
A romantic and melodious love theme that evolves over the course of the film from random ticklings of the piano keys to a sweeping full-bodied orchestration.
"Hell and Back" from Hell and Back Again (J. Ralph):
Soulful, poetically worded, and given melancholy voice by Willie Nelson's country rasp, this track is a soothing epilogue to a wrenching character study.
"Life's a Happy Song" from The Muppets (Bret Mackenzie):
A bouncy opening number that signals the beginning of a laugh-out-loud romp, and it even gets a heart-bursting reprise as the film's big finale.
"The Living Proof" from The Help, "Pictures in My Head" from The Muppets,
"The Keeper" from Machine Gun Preacher