It's my recommendation for foreigner who wishes to know more about Soviet cinema. I didn't include Russian (i.e. post-1991) films. 
I thought of top100 list but that would have too many absolutely unavailable for foreigners movies. This one also contain really rare films, but if you can find them you'll enjoy them!

Kino-eye (Dziga Vertov, 1924)
Strike (Sergey Eisenstein, 1925)
Battleship Potyomkin (Sergey Eisenstein, 1925)
The Girl with the Hat Box (Boris Barnet, 1927)
October (Sergey Eisenstein, 1927)
Arsenal (Alexander Dovzhenko, 1928 ) 
Man with a movie camera (Dziga Vertov, 1929)
Earth (Alexander Dovzhenko, 1930)
Salt for Svanetia (Mikhail Kalatozov, 1930)
Ivan (Alexander Dovzhenko, 1932)
Outskirts (Boris Barnet, 1933)
Three songs about Lenin (Dziga Vertov, 1934) 
Alexander Nevsky (Sergey Eisenstein, 1938 ) 
Ivan the Terrible (Sergey Eisenstein, 1944)
The Forty-first (Grigory Chukhrai, 1956)
The Cranes Are Flying (Mikhail Kalatozov, 1957)
Ballade of a soldier (Grigory Chukhrai, 1959)
Clear Heaven (Grigory Chukhrai, 1961)
Ivan's Childhood (Andrey Tarkovsky, 1962)
Shadows of Forgotten Ancestors (Sergey Parajanov, 1964)
I am Cuba (Mikhail Kalatozov, 1964)
I am twenty (Marlen Khutsiyev, 1964)
Long Happy Life (Gennady Shpalikov, 1966)
Beware of the Car! (Eldar Ryazanov, 1966)
July Rain (Marlen Khutsiyev, 1966)
Brief Encounters (Kira Muratova, 1967)
Sayat Nova (Sergey Parajanov, 1968 ) 
Andrey Rublyov (Andrey Tarkovsky, 1969)
Check-up On the Roads (Alexei German, 1971)
A Long Goodbye (Kira Muratova, 1971)
You and Me (Larisa Shepitko, 1971)
Irony of Fate (Eldar Ryazanov, 1975)
Mirror (Andrey Tarkovsky, 1975)
Twenty Days Without War (Alexei German, 1976)
Ascent (Larisa Shepitko, 1976)
Ordinary Wonder (Mark Zakharov, 1978 ) 
Stalker (Andrey Tarkovsky, 1979)
That Munchhausen (Mark Zakharov, 1979)
A Fox Hunt (Vadim Abdrashitov, 1980)
The Train Has Stopped (Vadim Abdrashitov, 1982)
Nostalghia (Andrey Tarkovsky, 1983)
Epilogue (Marlen Khutsiyev, 1983)
Parade of planets (Vadim Abdrashitov, 1984)
The Legend of the Suram Fortress (Sergey Parajanov, 1984)
My Friend Ivan Lapshin (Alexei German, 1984)
Plumbum, or The Dangerous Game (Vadim Abdrashitov, 1986)
The Lonely Human Voice (Alexander Sokurov, 1987)
Ashugi Qaribi (Sergey Parajanov, 1988 ) 
The Days of Eclipse (Alexander Sokurov, 1988 ) 
The Asthenic Syndrome (Kira Muratova, 1989)

+

Nine Days in One Year (Mikhail Romm, 1961)
I Step Through Moscow (Georgi Daneliya, 1963)
Father of a soldier (Rezo Chkheidze, 1964)
Ordinary Fascism (Mikhail Romm, 1965)
No Crossing Under Fire (Gleb Panfilov, 1967)
Falling Leaves (Otar Iosseliani, 196 
Don't Grieve (Georgi Daneliya, 1969)
Byelorussia Station (Andrei Smirnov, 1970)
The Beginning (Gleb Panfilov, 1970)
Pastorali (Otar Iosseliani, 1975)
Slave of Love (Nikita Mikhalkov, 1976)
The Tree of Desire (Tengiz Abuladze, 1977)
Unfinished Piece for Mechanical Piano (Nikita Mikhalkov, 1977)
Five evenings (Nikita Mikhalkov, 1979)
Come and See (Elem Klimov, 1985)