There is too much. TOO MUCH... And they like to change. I love that woman's music so damn much. I'll try to post only those which have always been my favorites:
forgiveness - it's something touching, but also peaceful and harmonizing in this song... Everything here is just perfect - arrangement, lyrics (simple and beautiful), Ayu's voice... I'm never tired of this song.
Duty - incredible atmosphere which any other Ayu's song doesn't have IMO. Composition and lyrics - A+
End of the World - I love how both arrangement and Ayu's voice is dramatic here. I've always wanted it to have its own PV T^T
Don't look back and
Sexy little things:
The most unique Ayu's song ever! There are no words to describe how perfect they are.
untitled ~for her~ - man, it grown in me so much... That song is just beautiful.
WHATEVER (LOVEppears ver.),
Real me,
rollin' and
LOVE'n'HATE:
my favorites in terms of catchiness. I've had them on repeat many times.
rainy day - Ayu's voice here is

I wouldn't mind an accapella or acoustic version of it. Composition is simply wonderful.
SURREAL - one of my first crushes and one of her best lyrics
NEVER EVER,
Microhpone and
Rule:
probably my fav rock songs of hers? Probably. And Rule remix is the best ever.
GAME and
HAPPY ENDING (MY STORY Classical versions):
I thought it's impossible to make them better than original versions, which are absolutely great... I was wrong.
evolution - the best from Ayu's classics.
A Song for ×× ''030213 Session #2'' - the only version of that song I love. And it's already epic.
from my letter - I don't know, I have such a sentiment to it! Very relaxing and soothing, makes me calm (

)
Trust - Her voice is so appealing to me, in both ASfxx and A BEST versions!
TO BE and
walking proud:
have a special meaning to me.
LOVE ~Destiny~ and
Dolls
My hidden jems, simply wonderful <3 Deserve much more love!
talkin' 2 myself - that song just kicks asses.
fated - my all-time favorite rock ballad from Ayu!
Free & Easy - a bit of my love for it has gone but I still love it
GREEN - my favorite oriental song from her, has a peaceful and romantic feeling.
AUDIENCE - I love its energy!