Well off the top of my head some films I'd love to watch again for any of the reasons A mentioned would be 

Diary of a Country Priest (Bresson)
The Mirror (Tarkovsky)
All About My Mother (Almodovar)
Blow-Up (Antonioni)
The General (Keaton)
The Awful Truth (McCarey)
Breaking the Waves (Von Trier)
The Apu Trilogy (Ray)
In a Lonely Place (Nicholas Ray)
The Apartment (Wilder)
Persona (Bergman)
Rear Window (Hitchcock)
Natural Born Killers (Stone)
To Be or Not To Be (Lubitsch)

I know there are more, but these are all films for one reason or another I'd like another look at.