There's a lot of contemporary/poppy music available on Youtube which is based on Psalm 19. I'm feeling a bit sick today, and then ... it's a bit tough for me to listen to Hillsong United stuff ... so if you want to find this for Psalm 19, you'll have to go looking yourself this time ;) .
The best-known rendition of this Psalm is probably Haydn's in Die Schopfung (the Creation). Here is the piece itself: http://www.youtube.com/watch?v=9LMsYlyAvC0 . A longer video, with William Christie (excellent for this period of music) is here - http://www.youtube.com/watch?v=Q5RHDwdaanQ - the portion with Psalm 19 in it is at "Day 4." Interesting here also is the commentary the Wikipedia has regarding this movement of The Creation:
No. 13. Die Himmel erzählen die Ehre Gottes (The heavens are telling the glory of God)
The mightiest of the choruses of The Creation and a popular favorite. Haydn's century, following on the discoveries of Newton but preceding those of Darwin, was the heyday of the view that an orderly universe—particularly the mathematically-governed motion of the heavenly bodies—attests to divine wisdom. Haydn, a naturally curious man, may have had an amateur interest in astronomy, as while in England he took the trouble to visit William Herschel, ex-composer and discoverer of Uranus, in his observatory in Slough.
"Die Himmel erzählen" is not in the home key of Part I, C minor, but is instead in C major, showing the triumph of light over dark. It begins with alternation between celebratory choral passages and more meditative sequences from the three vocal soloists, followed by a choral fugue on the words "Und seiner hände Werk zeigt an das Firmament", then a final homophonic section. ("The wonder of his works displays the firmament" is the English text here, with word-order calqued from the German, but somewhat awkward compared to the Authorized Version's "And the firmament sheweth the handywork of God".) The unusual intensity of the ending may be result of Haydn's piling of coda upon coda, each occurring at a point where the music seems to be about to end.
End of the fourth day.
I found one video with an older Italian guy singing something Gregorian which is at least partially based on Psalm 19. There's just something about this guy, sitting alone behind his electronic organ in a somewhat cramped room, with his beautiful voice, praising God with this psalm. He has a very good voice for doing solo Gregorian singing.
An organ piece by Allesandro Marcello (Italian woman, 1669-1747 - Bach knew of her work): http://www.youtube.com/watch?v=UEcBn2c0e1k
Well, one contemporary piece: The Twinkling Stars are a contribution from the Tamil Christian Contemporary Music scene. Here they sing, both in Tamil and in English (see if you can spot the transition) a beautiful hymn based on the first line of this song, with synthesizer and guitar accompaniment, in a music video featuring synchronized hand and head motions. http://www.youtube.com/watch?v=4H_XcaRG4vQ . Actually I have to hand it to these ladies - with just a guitar, a synthesizer, and a video camera, they're doing what they can to praise God, and it is very joyful music indeed.