The history of cinema is so enormous, so vast that it's injustfull to answer such a question with one movie. There are so many great movies that, so well made that to name just one movie to be greatest of all would be unfair. I love THE GODFATHER 1 & 2, both are well written, well directed and well acted. The character arc of michael in the first movie is the best I've ever seen. But i also love BLADE RUNNER, the world that RIDLEY SCOTT has created is unforgettable. that movie has grown into me, the more I watch it the more I respect it. On a side note , I liked the sequel too, Denis Villeneuve has done really done justice to the original.
Now, I can name alot of movies but what i can't do is pick just one. And I don't think any cinephile could do that. So here are some movies that I feel proud to have watched.
THE GODFATHER 1&2
PSYCHO
VERTIGO
THE SHINING
ONE FLEW OVER THE CUCKOO'S NEST
THE SHAWSHANK REDEMPTION
BLADE RUNNER
THE DEPARTED
TAXI DRIVER
GOODFELLAS
SERPICO
DOG'S DAY AFTERNOON
THE DEVIL'S ADVOCATE
2001: A SPACE ODYSSEY
THE DARK KNIGHT TRILOGY
MEMENTO
DAS BOOT
STALKER(ANDREI TARKOVSKY)
SICARIO
SEVEN
FIGHT CLUB
THERE WILL BE BLOOD
THE MASTER
These are all some must watch flicks.