It seems like most love songs are pretty sappy so the good stuff really stands out:

Just in Time by Styne, Comden and Green.
Love Walked In & Our Love is Here to Stay by George and Ira Gershwin.
If I Needed You by Townes Van Zandt.
For All We Know the one by Harold Arlen(?).
Anachie Gordon, a sad one.
Jock O'Hazeldean
Flow Sweet River Flow by Ewan McColl.