Very difficult to remember, but here's my list of the 10 best films that were shown for the first time in 2004. Alpha order only.

Control Room - Jehane Noujaim 
Dare mo shiranai - Hirokazu Koreeda 
De Fem benspnd - Lars von Trier 
Dogville - Lars von Trier 
The Dreamers - Bernardo Bertolucci 
Elephant - Gus van Sant 
Histoire de Marie et Julien - Jacques Rivette 
Notre musique - Jean-Luc Godard 
Otets i syn - Aleksandr Sokurov 
Panj asr - Samria Makhmalbaf