I have a good deal of a capella choral music of the religious bent (mostly Tallis Scholars and the Hilliard Ensemble), but setting those aside for the moment here's what I could find on my computer, broken down by language and origin (and now edited to fix HTML):
I also have a CD of Latvian traditional folk music that's mostly a capella, but I'd have to listen to it and winnow it down because some of the songs have instrumentals that slip in towards the end.
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English
Stan Rogers - Barrett's Privateers (sea shanty)
Stan Rogers - Rolling Down To Old Maui (sea shanty)
Mary McPartlan - Slieve Gallion Braes (folk music)
Tallis Scholars - A Robyn, Gentyl Robyn (madrigal)
Norwegian
Arve Moen Bergset - Gamle Gullbrand (folk music)
Arve Moen Bergset - Eg Var Liten (folk music)
Italian
King's Singers - Il bianco e dolce cigno (madrigal)
King's Singers - Or si rallegri il cielo (madrigal)
German
King's Singers - Ach, weh des leiden (madrigal)
Latin
Tallis Scholars - Spem in alium (40-part motet)
I also have a CD of Latvian traditional folk music that's mostly a capella, but I'd have to listen to it and winnow it down because some of the songs have instrumentals that slip in towards the end.