I am happy to point readers to an extensive list of sources for audio files of a cappella hymn singing, gathered on one page by the Church of Christ at Kuala Lumpur, Malaysia. Though the Internet is put to many foolish and often harmful uses, like most technologies it is a great blessing if put in the service of God. It is heartwarming to know that our brothers and sisters in Kuala Lumpur--whom I am likely never to meet in this life--share a love of the Lord and of singing His praise, and have taken the time to put together this list of resources and share it with the world.
In particular I recommend the resources associated with the College Church of Christ in Searcy, Arkansas, which includes a number of recordings of the Harding University choral groups. Though I love the recordings of live congregational singing as well, for the purposes of learning hymns it is often good to have access to a recording of a hymn sung by a trained group, singing just the notes as written and in balanced numbers on the parts.
Another resource here to which I am particularly partial is the archive of recordings from the Great Songs Chapel at Oklahoma Christian University. This began a few years ago as an alternative for those who wished to sing the traditional repertoire of hymns and gospel songs, much like the "Music Chapel" at Lipscomb University (so called from the fact that it was overseen by the music department faculty) which I had to privilege to lead many times. I am glad to say that the Great Songs Chapel is well attended, and if you listen to the recordings from this past year you might just catch the sweet alto voice of one particular freshman student--though it probably takes a father's ear to pick it out.
I hope these links will be a blessing to others as they have been to me! I am currently working on another installment of the series on the history of a cappella singing, which is taking much longer than expected. Hopefully that will be posted by the end of this month.