Some of my favorites:

Salutation of the Angel -- 15th century, to a tune almost identical to "Bring Us in Good Ale"

Chrisimas Day -- Trad. English:
There was a pig went out to dig,
Chrisimas day, Chrisimas day,
There was a pig went out to dig
On Chrisimas day in the morning.
. . .and so forth, through several animals and agrarian activities.

Personent Hodie -- from the Piae Cantiones, 1582. Simply lovely.

Entre le boeuf et l'ane gris -- Trad. French. One of my favorite Christmas melodies.

Come Mad Boys, Be Glad Boys -- Trad. English. The tune is the same as "Bonnie Sweet Robin", which I think is a 16th or 17th century Engish country dance tune.

Blessed Be That Maid Marie -- Trad. English, the tune is almost identical to Staines Morris, another old English dance tune.

Gloria Ad Modem Tubae -- by Guillaume Dufay, 15th century. A glorious, weird cannon.

John