I am particularly fond of the poems by Rumi, a 13th-century Sufi mystic, but haven't heard any of them set to music. Many of his works can be found translated at
this site. Beware of typos. I've fixed a few in the following.
One example:
'Tis light makes colour visible: at night
Red, green, and russet vanish from thy sight.
So to thee light by darkness is made known:
Since God hath none, He, seeing all, denies
Himself eternally to mortal eyes.
From the dark jungle as a tiger bright,
Form from the viewless Spirit leaps to light.
Another:
Those who don't feel this Love
pulling them like a river,
those who don't drink dawn
like a cup of spring water
or take in sunset like supper,
those who don't want to change,
let them sleep.
This Love is beyond the study of theology,
that old trickery and hypocrisy.
If you want to improve your mind that way,
sleep on.
I've given up on my brain.
I've torn the cloth to shreds
and thrown it away.
If you're not completely naked,
wrap your beautiful robe of words
around you,
and sleep.
And one more (I can almost hear the music to this one!):
How should the soul not take wings
when from the Glory of God
It hears a sweet, kindly call:
"Why are you here, soul? Arise!"
How should a fish not leap fast
into the sea from dry land
When from the ocean so cool
the sound of the waves reaches it?
How should the falcon not fly
back to his king from the hunt
When from the falconer's drum
it hears the call: "Oh, come back"?
Why should not every Sufi
begin to dance atom-like
Around the Sun of duration
that saves from impermanence?
What graciousness and what beauty?
What life-bestowing! What grace!
If anyone does without that, woe --
what err, what suffering!
Oh fly, oh fly, O my soul-bird,
fly to your primordial home!
You have escaped from the cage now --
your wings are spread in the air.
Oh travel from brackish water
now to the fountain of life!
Return from the place of the sandals
now to the high seat of souls!
Go on! Go on! We are going,
and we are coming, O soul,
From this world of separation
to union, a world beyond worlds!
How long shall we here in the dust-world
like children fill our skirts
With earth and with stones without value,
with broken shards without worth?
Let's take our hand from the dust grove,
let's fly to the heavens high,
Let's fly from our childish behaviour
and join the banquet of men!
Call out, O soul, to proclaim now
that you are ruler and king!
You have the grace of the answer,
you know the question as well!
. I have no idea how accurate her pronunciation is - her English and Spanish sounded fine to me. 
I would love to hear some settings for many of his works in the original.