I have a long list the ones that make me cry are

:
Still alone (this song gets to me every time

)
SCAR
Seasons used to make me cry
Fated
Together when
Hanabi ~episode II~
Memorial Address (seeing her perform it makes me cry too)
HEAVEN is just beautiful
Hope or Pain
Moments (the lyrics are so beautiful)
HANABI (the lyrics and the little beat get to me)
over
Jewel (just loving someone like this song describes it is amazing)
Ayu writes wonderful lyrics me and my sis agree that everytime we feel sad or want to get or feelings out we listen to ayu. I know its funny

but yeah. I especially like how ayu records sad songs because she incorporates that sadness and panfulness and it makes the songs much more impacting