Genesis
Exodus
Leviticus
Numbers
Deuteronomy
Job
Psalms
Proverbs
Ecclesiastes
Song of Songs
Judges
Ruth
1 Samuel
2 Samuel
It is possible that David knew about or had access to some of these, although most would not have been in their written form as we know them today. King David himself is traditionally the credited author of many Psalms included in the Old Testament books of the Bible.