I'm just in that kinda mood.
Just to give you a gauge of what movies I like and find adequately sad: Awakenings, Eternal Sunshine of the Spotless Mind, the documentaries The Bridge and About a Son, Oldboy (2003), and the Sixth Sense I actually find really sad too.
You asked for "a" film -- and I give you 13 -- sorry
but I really like every one of them.
"magnolia"
"The Vanishing" ("Spoorloos") -- the original
"Elephant" (Gus Van Sant's film)
"What's Eating Gilbert Grape" (what a marvelous performance by Leonardo DiCaprio)
-- some superb-to-me films directed by Michael Haneke:
"The Seventh Continent"
"Benny's Video"
"71 fragments of a chronology of chance"
"Funny Games" (the 1997 original, not the American remake)
"Pack of Lies" -- (Teri Garr, Ellen Burstyn, Alan Bates)
"Ordinary People"
"Vera Drake"
"Heavenly Creatures"
"Dancer in the Dark"