eldalieva; 1,2,7 and 8 on your list would all be in my top 100.

Difficult to separate favourite and greatest. My favourites are in my profile. Greatest? 

Sansho the Bailiff (Mizoguchi- exquisite beauty and aching poignancy)
Story of the Late Chrysanthemums (Mizoguchi- a work of extraordinary experimental genius as well as usual mastery of composition, camera movement, lighting etc)
Andrei Rublev (Tarkovsky)
Sunrise (Murnau)
La Regle du Jeu (Renoir)
Mirror (Tarkovsky)
Tokyo Story (Ozu)
Maborosi (Kore-eda- a hidden gem)
2001: A Space Odyssey (Kubrick)

Seven Samurai, Vertigo, Citizen Kane, Battleship Potemkin of course have fair claims for inclusion. In international polls, Citizen Kane, La Regle du Jeu and Vertigo have consistently been at or near the top in recent years.

The Producers and the Tories? well, we seem to agree on one of the two, Gaz.