“Ave Verum Corpus” by Francis Poulenc (you may need to turn the volume up a bit for this one)

“Salve Regina” by Francis Poulenc

“Ubi Caritas et Amor” by Maurice Duruflé

“Notre Père” by Maurice Duruflé

I’ll probably add more later.  These are some of my favorites.

[UPDATE]: A reader recommended “O Sacrum Convivium” by Olivier Messiaen.  It’s a haunting piece, and I’ve never heard harmonies quite like those–I’m impressed.  [UPDATE 2]:  I changed this link to a different version recommended by a reader.  You might need to up your volume a bit.  I agree that it is magnificent.

On a rather more secular note: I simply can’t fail to share this treasure from my own generation.  It too is a cappella… but also so much more!