The Responsorial Psalm is not just any song.  These are settings of scripture, taken from the book of Psalms.  In the liturgy, the psalm reflects the people's response to the first reading.
Psalm 25:  I Lift Up My Soul (Manion)
Psalm 25:  To You, O Lord (Haugen)
Psalm 34:  I Will Always Thank the Lord (Soper)
Psalm 34:  Taste and See (Haugen)
Psalm 128:  Blest Are Those (Haugen)
Psalm 128:  O Blessed Are Those (Inwood)
Psalm 145:  I Will Praise Your Name (Haas)