Arvo Part, Jean Langlais, Jehan Alain, Charles Tournemire

Kevin Allen. All of his stuff is great, but here's one of my favs:

http://www.youtube.com/watch?v=Ykqr1awLxIY#t=19s

Stravinsky Symphony of Psalms (1930) 3rd movement, Psalm 150

Ben, I think he might have missed the cutoff - was this from the 21st century? That will be another thread. ;-)

I really like Ola Gjeilo's music, although this is 21st century not 20th. The piece below is his setting of Ubi Caritas
http://youtu.be/zvI5sNucz1w

I also like the things already mentioned (i.e. Durufle, Rachmaninoff, Lauridsen). I went to undergrad at a Wesleyan college where I was introduced to a lot of Randall Thompson's music which is very beautiful. Below are his Alleluia and Last Words of David. Additionally he has a set of pieces entitled "The Peaceable Kingdom" which I enjoy.
http://youtu.be/2iCwCTv8heA
http://youtu.be/ssOihxIYhdg

Again, more recently, Eric Whitacre has just published his own setting of Alleluia which is very nice.
http://youtu.be/Rak_rJLG49k

examples... hmm... (ugh, too much work...)
Part: Beatitudes (also, there was a thread about him on here recently, with other good suggestions)
Langlais: Ave Maria Ave Maris Stella, Acclamations & Improvisation from Suite Medievale
Alain: Postlude pour l'office de Complies, Litanies
Tournemire: Hard to think of anything in particular. I'm mostly familiar with a few tiny (rather obscure) movements from his L'Orgue Mystique. They're fabulous especially in the context of what they were meant for - Mass.

There's lots more (and those aren't necessarily the "best" of each composer)... those are just the few off the top of my head that I'm more familiar with.

@Gregp
I stand corrected :) I was just thinking new music...

Holst's "The Planets" is another great piece.

What also annoys me is that I couldn't think of a great "contemporary" work (truly contemporary, not aping classic styles with modal or add2 chords) that was written in my lifetime (80s or later).

Poulenc's Vinea mea electa
http://www.youtube.com/watch?v=v0kwNhNcJnA

Love, love the Barber - love Durufle and really like/love Leo Nestor's setting of just about anything. But I must disclose that I've studied with him and sung under his direction a lot.

Recordings of his stuff are hard to find, I wish I could post, but not much out there on the fly...
I particularly like his "Come Ye Sinners Poor and Needy" and he just wrote a commissioned piece that - I confess - I was in his chamber choir when he premiered it:
This is the Hour of Banquet and of Song. http://www.sheetmusicplus.com/title/This-Is-the-Hour-of-Banquet-and-of-Song/19844055

Also, there are many good composers on this forum: Charles Giffen, Paul O., Francis K., Andrew M., etc. etc. As a matter of fact, I've been fortunate to use work by all of these generous composers.

AND, I also like Richard Rice's settings/compositions, Kevin Allen, and a host of others - I use their work every week just about.

Dupre's Ave verum is particularly beautiful.

Wow, thanks for all those, Charles! My wife and I had the opportunity to go to the World premiere run of his opera "Paradise Lost" at the Lyric Opera of Chicago in 1978. I have to admit I was not impressed then, but I was young and foolish, so this is a great change to listen again and see what I've missed.

Poulenc 'Ave Verum'
Lennox Berkeley (Friend of Britten and Poulenc, and Nadia Boulanger) : Mass for Four Voices; Mass for Five Voices.

Well, the Threenody isn't intended to be Sacred Music in the sense of it being used within the context of liturgy- it is a concert piece and should be examined from that standpoint.

I have two problems with "20th Century Music" (by which I mean, the specific cluster of genres, not the period of time).

1) The philosophical questions about music are not very interesting and do not lead to interesting art.
Whether you're talking about timed silence or vacuum cleaners or stop-watch-conducted whispering, it isn't relevant (to me) that the piece "asks fundamental questions about the nature of music" or any other mumbo-jumbo along those lines. When the form IS the content, I stop caring, because a written description of the music becomes just as useful to the philosophical discussion as the experience of hearing or performing it.

So, that pretty much leaves me out of wanting to have anything to do with aleatoric music, or any of the "compositions" in the Cage school.

2) The philosophy underpinning much 20th C. Music is terrifying, and I want no part of it.
While point (1) deals with all the "is that really music" BS, point (2) is about the music that clearly is music, but which is downright terrifying in its artistic/philosophical implications. Since music is hard to talk about, I'll talk about theatre.
There is no question about whether Caligula (Camus) or Waiting for Godot (Becket) are legitimate plays in even a conventional sense. But the philosophy they portray, the world view they illuminate, is both false and terrifying. Because I like art and theatre, and have an interest in philosophy, I might go see a production of either one (if I knew it was going to be good), but I almost certainly wouldn't program them if I were a theatre's Artistic Director, and I would be somewhat wary about exposing my children to either one. As an angsty teenager, I found 20th C. theatre - Artaud, Camus, Beckett, Schaffer - to be... philosophically alluring in a way that today I might characterize as malevolent, possibly even diabolical.
I mentioned Schoenberg's Pierrot Lunnaire above. That's a perfect example in music. Terrifying really is about the only word to describe it. As a work of art is absolutely amazing. But it is also, in my opinion, dangerous. I'm glad I discovered it in college, and not when I was an angsty teenager.

I may have overlooked them, but am surprised that Howells, Britten & V-W are not listed. Also the Poulenc motets. And such contemporaries as Whitacre & cet., plus quite a few Britons currently crafting outstanding sacred choral music.
As an aside, I typically get bright-eyed nods of approval from fellow musicians when I point out that there is a vast difference between so-called 'contemporary music' and modern music.

Benjamin Britten's "A Hymn to the Virgin"

I'm not really familiar with a lot of modern sacred music (or a lot of ancient, for that matter) since I've not really had a chance to do much of it, but I do like Biebl's Ave Maria.

http://www.youtube.com/watch?v=XVyCJlPiHFg

I do recognize the beauty of the Biebl, but while it blew me away the first time I heard it, the more it's been done, the more tedious it gets for me because of the repetition. Don't know why this affects me in this piece more than others that repeat, but I guess I sigh inwardly after the first Ave Maria as I realize there are two more just like it to get through...but if it's exquisitely sung, I'll endure it. I guess it just has to keep getting better to hold my interest! :)

Arvo Part, hands down.

His "Adam's Lament" (2011) is one of the greatest works I've heard in a long time -- highly recommend the ECM recording, which has some delightful other pieces on it.

Arvo Part, yes: Passio, and Kanon Pokajanen.

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http://forum.musicasacra.com/forum/discussion/8979/ave-maria#Item_10