Important Movies

1. Raiders of the Lost Ark: One of the most famous movies ever.

2. The Road Warrior: Helped make Mel Gibson a star and has been greatly influential on subsequent post-apocalyptic films. It's also probably the most well-known Australian film.

3. Das Boot: Highly acclaimed. I would also imagine ever submarine film since as looked to Das Boot for inspiration.

4. The Evil Dead: I'm not really a fan, but there's no denying Raimi created something iconic working with very little.

5. Heavy Metal: Alright, this is certainly a very trashy pick, but the notion of using animation to tell a story full of sex and violence was pretty novel back in 1981, and I think that should be acknowledged. The film has also spawned a pretty dedicated cult following and a bunch of filmmakers have endorsed the movie in some way or another, including: David Fincher, Guillermo del Toro, Zack Snyder, Gore Verbinski, James Cameron, Mark Osborne, and Robert Rodriguez.

Honourable Mentions:

An American Werewolf in London: The make-up effects are rightfully famous, but the rest of the film seems a lot less noteworthy.

Blow Out: It received great reviews in its day and Tarantino has spoke of its influence on him, but otherwise the movie seems kind of forgotten.

Thief: Michael Mann's first film, but not one well known.

Scanners: The head exploding is pretty cool.

My Dinner with Andre: People know of this movie, but I think far more know the title than have actually seen it.

1. Raiders of the Lost Ark
2.The Evil Dead
3. Escape from New York
4. An American Werewolf in London
5. Arthur
6. Chariots of Fire
7. The Great Muppet Caper
8. The Fox and the Hound

Raiders is obvious
Das Boot is a pretty influential war film
Evil dead made waves in the horror community
dinner with andre because no one expected it to work
Road warrior - a landmark action film

An American Werewolf in London = first vivid onscreen werewolf transformation
Chariots of Fire = 4 Oscars including BP
Excalibur = Wonderful cinematography, costume and set design
Raiders of the Lost Ark = just a classic
Heavy Metal = really cool motion capture animation and soundtrack

Honorable mention:

Ragtime = Cagney's last silver screen role (he had a TV role after this)
On Golden Pond = Fonda's last silver screen role (he also had a TV role after this)
Time Bandits = a wonderful madcap fantasy with little people
For Your Eyes Only = only transsexual Bond girl

Sorry sorry! Kind of forgot about this thread....

I vote Clash of the Titans!

Other entries forthcoming.

I think Jason and the Argonauts is a strong enough representation for Ray Harryhausen.

I can guarantee you that most people under 30 have never seen My Dinner With Andre. They know what it is based on the jokes and references you mentioned. It's the Kardashian of movies. It's famous for being famous.

The Road Warrior
An American Werewolf in London
Clash of the Titans
Das Boot
Raiders of the Lost Ark

You're not wrong, it was definitely one of those movies like Clerks which made a lot of young filmmakers think "wow, you really don't need tones of expensive stuff in order to make a great movie.  

Rebel Without a Cause
The Seven Year Itch
The Night of the Hunter
East of Eden
Blackboard Jungle

All That Heaven Allows (Highly influential melodrama which directly influenced later movies like Ali: Fear Eats the Soul and Far From Heaven)
The Blackboard Jungle (The fist movie about a white teacher going into an inner city school.  Not exactly the best legacy, but this kind of social realism was a big deal in the Hollywood of the 50s)
Rebel Without a Cause (the movie that cemented James Dean as an Icon of cool)
Rififi (a classic heist movie, it and The Killing are the prototypes of the highly choreographed heist sequence that gets pulled off perfectly)
The Night of the Hunter (Just a stone cold classic)

Honorable Mentions:
The Seven Year Itch (played a role in Marylin Monroe's status as a sex symbol, but the years have not been kind to the movie.  The whole thing makes very little sense under modern sexual mores and it will probably seem even stranger in future years.  Would still probably be worth considering in a weaker year.)
Smiles of a Summer Night (the film that brought Ingmar Bergman to international attention)
Marty (One of the first "small" movies to win Best Picture, definitely made a statement about Hollywood glamour.  Not all that impressive when removed from its context.)
Pather Panchali (The first of Satyajit Ray's famous Apu trilogy)
Diabolique (Very cool thriller with a famous twist ending)
The Man With the Golden Arm (First Hollywood movie about drug addiction)
The Ladykillers (Pretty famous Ealing comedy)

The Night of the Hunter - Iconic in so many ways, a masterpiece of the decade.

Pather Panchali - The pinnacle of Indian cinema, a beautiful film of despair and life in poverty-stricken India after British rule. Masterpiece.

Night and Fog - Yeah it's only like 20 minutes long, but it may also be the greatest documentary ever made. Disturbing and entrancing.

Rebel Without a Cause - Not as good as advertised, but it's influence and pop culture standing due to Dean's performance is undeniable. Plus we learned that rich white kids in the '50s had no problem playing chicken and driving their cars off cliffs just to make a point.

All That Heaven Allows - I love me some schmaltzy Douglas Sirk, the master of the melodrama. Great film? No, but very good and influenced numerous films. Plus Tarantino loves the film.