Thanks to Recta Ratio for listing some of his favorite Carols since I found one that was a childhood favorite. The Boar’s Head Carol is an English carol that also has Latin verses and I found a free mp3 version of it that is quite good on this page.
The same site also has some other excellent Carols also in mp3 format.
Angelus ad Virginem – Bonus points for it being totally in Latin and being cool to replay on the Annunciation. (The page provides a side by side translation)
Here are mp3 versions of Rudolphus rubrinasus (Rudolf the Rudolph the Red-Nosed Reindeer) in Latin.
Rudolphus rubrinasus fulgentissimo naso,
vidisti et si eum dicas quoque candere.
Omnes tarandi ceteri ridebant vocantes nomina;
non sinebant Rudolphum interessa ludentes.
olim crassa nocte Christi, Nicolaus it dictum:
“ Rudolphe, naso tam claro, agesne traham meam?”
Qui tum tarandis amor conclamantibus eum,
“ Rudolphe, rubrinase descendes historia!”
Update: Corrected composer of Ave Maria as per reader comment.