I wasn't sure if you wanted to include great song versions that are only on singles...
The Green/Days and Mirrorcle World singles are a great buy because they have special 10th Anniversary tracks. These are: To Be, Love: Destiny, Depend On You, and You.
'A Song Is Born' single contains her duet with Keiko. This version does not appear on any of Ayu's albums
Also, if you are only counting her Studio albums there is one song that appears only on it's single and her 'A Complete'. That song is 'Endless Sorrow'. Her studio album 'I am...' has the ~gone with the wind version~.
'A Complete' also has her Chinese version of 'Who'
Great song!