"Cucurrucucú Paloma" by Caetano Veloso. This version is known through "Habla con ella", a movie by Pedro Almodóvar".

Lyrics

Dicen que por las noches
no más se le iba en puro llorar
Dicen que no comía
no más se le iba en puro tomar
Juran que el mismo cielo
se estremecía al oír su llanto
cómo sufrió por ella
y hasta en su muerte la fue llamando

Ay, ay, ay, ay, ay cantaba
Ay, ay, ay, ay, ay gemía
Ay, ay, ay, ay, ay cantaba De pasión mortal moría
Que una paloma triste
muy de mañana le va a cantar
a la casita sola
con sus puertitas de par en par

Juran que esa paloma
no es otra cosa más que su alma
que todavía espera
a que regrese la desdichada
Cucurrucucú paloma, cucurrucucú no llores
Las piedras jamás, paloma
¿Qué van a saber de amores?
Cucurrucucú, cucurrucucú
Cucurrucucú, cucurrucucú
Cucurrucucú, paloma, ya no le llores 

Harry Belafonte - 1957

An older known version, yet not the original, by Harry Belafonte.

YouTube

Translation

They say that at nights
all he could do was cry all the time
they say he won´t eat
all he could do was drink at all times
they swear that heaven itself
would tremble hearing his crying
He suffered so much for her
that even on his death he was calling her

ay, ay, ay, ay, ay, he cried
ay, ay ay ay ay, he sobbed
ay ay ay ay ay he sang
from a deadly passion, he died

That a sad sparrow
early in the morning goes to sing
at the lonely little house
with it´s liitle doors wide open
They swear that that sparrow
is nothing else than his soul
still waiting for her return

Cucucrrucucu, sparrow
cucucrrucucu, don´t cry
stones will never, sparrow
know anything about love

cucurrucucu, cucurrucucu
cucurrucucu, sparrow don´t cry