Just today registered here and finding this thread, I'm probably a bit late to post my list for best cinematic experiences with new films in 2006, but I decided to do it nevertheless. These are my favourite new movies in 2006 (most of them got an official theatrical release here in germany, some of them I have seen at film festivals), using the international distribution titles and maybe the first three films on my list are some very personal favourites, but that's what this kind of lists are for in my opinion (either you can't claim the "best" films anyway), so here we go:

1. L'AUDITION (Luc Picard)
2. MIAMI VICE (Michael Mann)
3. SCIENCE OF SLEEP (Michel Gondry)
4. BATTLE IN HEAVEN (Carlos Reygadas)
5. THE NEW WORLD (Terrence Malick)
6. HIDDEN (Michael Haneke)
7. THE HOST (Joon-ho Bong)
8. WINTER JOURNEY (Hans Steinbichler)
9. THE METHOD (Marcelo Pieyro)
10. SHORTBUS (John Cameron Mitchell)
11. CHILDREN OF MEN (Alfonso Cuaron)
12. SUMMER IN BERLIN (Andreas Dresen)
13. SILENT HILL (Christophe Gans)
14. INVISIBLE WAVES (Pen-Ek Ratanaruang)
15. BROKEBACK MOUNTAIN (Ang Lee)
16. SYMPATHY FOR LADY VENGEANCE (Chan-wook Park)
17. TIME TO LEAVE (Franois Ozon)
18. PURE HEARTS (Kenneth Kainz)
19. THE DEPARTED (Martin Scorsese)
20. REQUIEM FOR BILLY THE KID (Anne Feinsilber)

And in addition four really great movies that unluckily only made it on DVD (plus with delay) in germany:

THE ORDEAL (Fabrice Du Welz)
SURVIVE STYLE 5+ (Gen Sekiguchi)
MYSTERIOUS SKIN (Gregg Araki)
KAMIKAZE GIRLS (Tetsuya Nakashima)