In no particular order; those in bold MUST BE SEEN IMMEDIATELY:

CLASSIC FILM NOIR
Double Indemnity (perfect script, genius acting; a film by the great Billy Wilder)
The Maltese Falcon
Laura
Gaslight
(with the young Ingrid Bergman)
The House on Telegraph Hill
The Big Sleep
Dead Reckoning
Key Largo
The Strange Love of Martha Ivers (Barbara Stanwyck, Kirk Douglas)
Sunset Boulevard
L.A. Confidential

CLASSIC AMERICAN ‘SCREWBALL’ COMEDIES
Ball of Fire (Barbara Stanwyck)
Bringing Up Baby
His Gal Friday

ROMANTIC
Casablanca
A Love Affair to Remember (Deborah Kerr, Cary Grant)
Frankie and Johnny (Michelle Pfeiffer, Al Pacino)
Scent of a Woman (the original one – L’Aroma di Donna – with Vittorio Gassman)
Roman Holiday
Funny Face

ITALIAN (a sea of genius, hard to be comprehensive; some favorites:)
All by Fellini, DeSica
The Bicycle Thief
Marriage, Italian-Style
Divorce, Italian-Style
Amarcord
8.5

All by Lina Wertmüller, esp. Swept Away, Seven Beauties, The Seduction of Mimi
Macaroni, with the older Jack Lemmon & M. Mastroianni
I Girasoli (The Sunflowers) (S. Loren & M. Mastroianni)

BRITISH (vast selection; these are some off-the-top-of-the-head favorites)
Julius Caesar (1954) – the young Marlon Brandon and Deborah Kerr
Anything with Alec Guinness, esp. The Card
Michael Caine: Pulp, Dirty Rotten Scoundrels
Anything with Colin Firth, esp. https://en.wikipedia.org/wiki/Conspiracy_(2001_film), Valmont, My Life So Far,
Harold & Maud
Anything by David Lean, esp. Brief Encounter, Odd Man Out et al
A Bridge Too Far

Being There (Peter Sellers)

FRENCH (this is the beginning of a vy long list)
L’Atalante
Hiroshima Mon Amour
The Umbrellas of Cherbourg
(with the young Catherine Deneuve)
Breathless (Jean-Paul Belmondo)
The Pianist, Venus in Furs, The Ninth Gate (Roman Polansky)
Never on Sunday, plus all the other Jules Dassin films
The Man Who Loved Women
Brotherhood of the Wolf (Vincent Cassel)

JAPANESE (not even scratching the surface)
Seven Samurai
Yojimbo
Rashomon
Twilight Samurai
Ikiru
Tokyo Story

etc
etc
etc

AUSTRALIAN
Age of Consent (UK/Australian; with James Mason and a very young Helen Mirren)
Boyhttp://www.imdb.com/title/tt1560139/
Shine

AMERICAN
Everything by Charlie Chaplin
Anything written or directed by Billy Wilder, esp. his films listed in the NOIR section, above, plus One, Two, Three (fantastic, perfectly entertaining, phenomenal dialogue; stars an older James Cagney)
Anything with the young Al Pacino, esp. The Godfather, I and II, Serpico, ‘Author, Author’, Looking for Richard, et al
All About Eve
The Apartment (the young Jack Lemmon and Shirley McLaine)
The Lady Eve
Anything by Stanley Kubrick, esp. The Killing (not about murder), Dr. Strangelove, 2001: A Space Odyssey, Barry Lyndon, Full Metal Jacket
Chinatown (Polanski, Nicholson, Dunaway, Quinn)
Apocalypse Now
Paper Moon (Ryan O’Neal, Tatum O’Neal)
Anything by Robert Altman, esp. M*A*S*H, Gosford Park, A Wedding, et al.
David Lynch (not for everyone)
Cool Hand Luke (the young Paul Newman)
The Bad News Bears (Walter Matthau, Tatum O’Neal)
Films by the Coen Brothers: Hudsucker Proxy; ‘O, Brother, Where Art Thou?’; The Big Lebowski
Films starring Kate Winslet, esp. Iris, Holy SmokeRevolutionary Road
Anything with William Holden, esp. Union Station, Stalag 17, The Proud and the Profane (also with Deborah Kerr), Sabrina (1954; also with Humphrey Bogart and Audrey Hepburn)
Network (Faye Dunaway, William Holden)
Restoration (Robert Downey Jr.)
Anything directed by Nick Cassavetes
Sweet Liberty (Michael Caine, Michelle Pfeiffer, Bob Hoskins, Alan Alda)
Lolita (with Jeremy Irons)
Soapdish
Bowfinger
Big Night (Isabella Rossellini)
The Princess Bride
Films by James Cameron, esp. The Abyss, Avatar, et al
Films by Mike Nichols, esp. Who’s Afraid of Virginia Woolf?, all his films feat. Meryl Streep, etc.
Love in the Afternoon (A. Hepburn, Gary Cooper)
It Happened One Night (Claudette Colbert, Gary Cooper)
Dodsworth
Five Easy Pieces (Jack Nicholson)
Best in Show (mockumentary)
Training Day, Man on Fire, Flight (Denzel Washington)
I Love You, Phillip Morris

SPANISH (I’m not an expert)
Luis Buñuel
Pedro Almodovar

WERNER HERZOG
Fitzcarraldo
The Enigma of Kaspar Hauser
Strosjek

Documentaries: Wings of Hope, Little Dieter Wants to Fly, The White Diamond, Happy People, etc

RUSSIAN
(only the best; excluding arthouse, i.e. Tarkovsky)
https://en.wikipedia.org/wiki/Anna_Karenina_(1967_film)
The Lady with the Dog (1960): https://en.wikipedia.org/wiki/The_Lady_with_the_Dog_(film)

https://en.wikipedia.org/wiki/Three_Poplars_in_Plyushcikha
https://en.wikipedia.org/wiki/The_Very_Same_Munchhausen
https://sh.wikipedia.org/wiki/Tihi_Don_(film)
https://sh.wikipedia.org/wiki/Kin-dza-dza!