The oldest secular song of Scandinavia: Drømte mig en drøm i nat from the Codex Runicus, a manuscript about the provincial law of Skåne around the year 1300. ( original and transcription). The text "Drømte mig en drøm i nat om silki og ærlig pæl" suggests a trochaic rhythm for the melody. Based on this short fragment, several musicians have tried reconstructions of the song: One can improvise on it, develop the melody further, add voices... Here you can listen to the reconstruction by Maja Marcussen which she was teaching together with Kåre Lie at the NHM 2008 in Lund.
The melody is well known in Denmark, because Denmarks Radio P1 has used the first 15 notes as an interval signal since 1931 (but omitted the melismatic part in the end).

Herr Tidmand (DgF 317), a ballad about the tax collector who is assasinated. Niss Stricker was teaching this ballad at the NHM 2010 in Gjøvik.

Herr Oluf han rider (DgF 47), another ballad from Niss's workshop. This one tells about the fateful encounter of sir Oluf with the fairies, and has close parallels in all Nordic countries and the rest of Europe. (Click here for some English versions.)

Jeg så en ulv en ræv en hare - another song from Niss' harp workshop at the NHM 2010. This song, quite popular among middle age reenactors in Scandinavia (e.g. here), is the Danish version of a traditional Occitan folk song whose first eight notes (repeated 4x) are identical with the beginning of the 13th century sequence Dies irae.

Hornfiffen fra Randers, a folk dance from Randers, Jutland. The tune, also known as "Soldier's Joy", exists in various versions in all Nordic countries and in Britain. In Norway, it has the following lyrics ( click here for English translation):
På Rommestad *) der brygger de så godt et øl
det romler rundt i magen som et hesteføll
og suser rundt i haue som en humledott
og ut igjennom rævva som et bøsseskott!

(* insert the name of your farm here)