The portion Chukat — Bamidbar/Numbers 19:1 – 22:1 — includes a bit of poetry sometimes called the “Song of the Well” (21:17-18):
Rise up, O well!
Sing out to it
Well, that captains dug
the people’s nobles delved it
with a scepter, with their walking stick.
In tractate Rosh Hashanah [New Year]), it is explained that the “Song of the Well” and the “Song of the Sea” (Exodus 15:1ff) were sung in the Temple on different weeks at the Shabbat afternoon sacrifice.
There are ten songs in all mentioned in the Tanach. In addition to these two, are the following:
Isaiah 30:29 (for Passover)
Deuteronomy 31:22 (Haazinu)
Judges 5:1 (Deborah’s song)
2 Samuel 22:1
2 Chronicles 6:1
2 Chronicles 20:21
Isaiah 42:10 (song in the world to come).
My source for this is The Book of Legends (Bialik/Ravnitzky). They cite Mekhilta, a compilation of midrash on Exodus.