These movies were recommended by two different people in the comments to my movie post.

Note: These recommendations are not mine. They are taken straight from the comments.

1776 - a musical about the days before the Declaration of Independence was authored and signed

Adaptation

Apocalypse Now 2 Babette's Feast

Auntie Mame -  because no one is funnier & faster than Cary Grant & Roz Russell.

Brother from another Planet – by John Sayle - SciFi mute guy in Harlem.

Citizen Kane

Conan the Barbarian 2 The Big Lebowski 5 Dogma - I credit this movie as being partly responsible for my conversion to Christianity.

Donnie Darko

Dune

The Englishman Who Went Up A Hill But Came Down A Mountain

The Fifth Element - This movie is so grossly underrated.

Hands on a hard body

Harold & Maude - Because it made love and sex and age seem glorious (& I have always believed, a la Maude, that everyone should be able to make their own music).

Hudsucker Proxy

The Journey of Natty Gann - This one's great. It's about a girl trying to find her father during the Great Depression. I think this was Disney's last good live-action film.

Life is Beautiful

The Mexican

Monsoon Wedding

Princess Mononoke

Singing in the Rain

Sliding Doors

Snatch

Songcatcher - it's about a woman from Pennsylvania, I think, who goes to the mountains of Appalachia (east TN, maybe?) to study the folk songs there. She discovers songs passed down in almost original form from Elizabethan England and thereabouts.

The Sure Thing - "Thoughts raced through his mind. Did she really want him? What had he done to deserve this bounty? Does God exist? Who invented liquid soap and why?"

Lone Star - by John Sayles

Tampopo

The Tao of Steve - love and wisdom from New Mexico - a comedy.

That Thing You Do! - co-starring (and written and directed by) Tom Hanks. He even wrote some of the music. A really wholesome and good movie about the rise and fall of a one-hit wonder band in 1964. Not a sour note in the whole movie.

Thirteenth Floor

This is Spinal Tap

Truly, Madly, Deeply - is a beautiful, intelligent, heart-wrenching ghost story. Intelligent and funny- one of Alan Rickman's best.

Truman Show

Unbreakable