Must haves? I'd include Eternal Sunshine all right. I connected strongly with Joel and Clementine, more than the characters in Human Nature or Being John Malkovich (which were good films).
What else? Let's see.
Topsy Turvey on the surface is about Gilbert and Sullivan putting together the Mikado. But it's really about the amazing amount of life and energy artists pour into their work.
Double Indemity is a classic film noir about a murder planned a femme fatale and insurance salesman. But the surprising element is the relationship between the salesman and an insurance adjuster at the same company.
Casablanca is a wonderful film about love and sacrificing that love for the greater good. Wonderful work by supporting actors like Dooley Wilson, Peter Lorre and Sydney Greenstreet.
Sunset Boulevard is about an aging actress trying to make a comeback with the help of a struggling writer and her faithful butler. It's amazing that this indictment of Hollywood greed got made when it did.
Peeping Tom was made around the same time as Psycho, but it makes the audience complicent in the murder, so it was despised and hated at the time it was released. The most sympathetic portrait of a serial killer I've ever seen.
Gone with the Wind is too sentimental about the scourge of slavery in antebellum south, but the performances of the actors make up for it. My favorite touch is they made Mammy the most intelligent and sensible character in the movie. The less said about Prissy the better.
The Wizard of Oz. A classic and amazing ensemble work with all five leads (all from vaudeville). Few movies have featured so many iconic characters. The special effects hold up great for a movie released in 1939.