Because there's nothing specific here to latch on to, I'll go ahead and post two recommendations each for a handful of different genres. Some are considered enduring classics, others are just some films that tickle me, and all are worth watching at least once in my opinion. I'm not going to bother going into detail on any of them unless someone asks, because that would really take a lot of time given how many films I'm listing.
Of course, these films are only the barest tip of the cinematic iceberg; there are hundreds of rec-worthy films out there, it only one would just take the time to look.
Drama
Wild Strawberries (Sweden, 1957, Dir. Ingmar Bergman)
8 ½ (Italy, 1963, Dir. Fredrico Fellini)
Comedy
Withnail & I (UK, 1987, Dir. Bruce Robinson)
You Can't Stop the Murders (Australia, 2oo3, Dir. Anthony Mir)
Romance
Smiles of a Summer Night (Sweden, 1955, Dir. Ingmar Berman)
3-Iron (Korea, 2oo4, Dir. Kim Ki-Duk)
Horror
The Beyond (Italy, 1981, Dir. Lucio Fulci)
In a Glass Cage (Spain, 1987, Dir. Agustí Villaronga)
Science Fiction
Solyaris (Russia, 1972, Dir. Andrei Tarkovsky)
Logan's Run (US, 1976, Dir. Michael Anderson)
War
Zulu (UK, 1964, Dir. Cy Endfield)
Stalingrad (Germany, 1993, Dir. Joseph Vilsmaier)
Western
High Noon (US, 1952, Dir. Fred Zinnermann)
The Wild Bunch (US, 1969, Dir. Sam Peckinpah)
Noir
M (Germany, 1931, Dir. Fritz Lang)
The Big Sleep (US, 1946, Dir. Howard Hawks)
Silent
Intolerance (US, 1916, Dir. D.W. Griffith)
Metropolis (Germany, 1927, Dir. Fritz Lang)
Documentary
Night and Fog (France, 1955, Dir. Alain Resnais)
The Atomic Café (US, 1982, Dirs. Jayne Loader, Kevin & Pierce Rafferty)
Animated
The Fantastic Planet (France, 1973, Dir. René Laloux)
The Old Man and the Sea (Russia, 1999, Dir. Aleksandr Petrov)
Cult Classic
The Warriors (US, 1979, Dir. Walter Hill)
Brazil (UK, 1985, Dir. Terry Gilliam)
Film Shorts
Un Chien Andalou (French, 1929, Dir. Luis Buñuel)
The Provider (US, 2oo3, Dir. Matt Smith)
"Other"
Salò, or The 120 Days of Sodom (Italy/France, 1975, Dir. Pier Paolo Pasolini)
Begotten (US, 1990, Dir. E. Elias Merhige)
~ jj ~