Here are mine, in no particular order:
Breakfast Club
Ferris Bueller’s Day Off
The Truman Show
Forest Gump
2001: A Space Odyssey
The Cube
Airplane!
The Cabinet of Dr. Caligari
Metropolis
Jurassic Park (1st)
I have pretty eclectic tastes 
General faves:
Amadeus
Casablanca
Chinatown
Citizen Kane
Henry V
The Maltese Falcon
On the Waterfront
Psycho
The Seven Samurai & The Magnificent Seven
The Silence of the Lambs
The Wizard of Oz
Best musical: The Sound of Music
Favorite Hitch: The 39 Steps, Dial M for Murder
Favorite comedies: This Is Spinal Tap, The Gods Must be Crazy
Best westerns: Unforgiven, The Man Who Shot Liberty Valence
I may not agree with the choices of others, but I will defend…uh, they can say what they want.
The Beast of War,(1988) : Horrific tale of the Russian Invasion of Afghanistan.
The Cabinet of Dr. Caligaro : Very early black and white horror film, with incredible artistic flare.
Pink Floyd The Wall : Dark and painful film.
Amelie : One of the most endeering films ever made
The Red Violin : An amazing film played out over many centuries.
Donnie Darko : Complex questions arrise from this coming of age yarn.
Trainspotting : Realistic drug story (imho)
Clerks : Still the strongest of the Kevin Smith films
The Fifth Eliment (SuperBit version) : Very good sci-fi, and an excellent film to show off your dvd system
– looking back it seems I have a slot left.
Jesus of Montreal : A passion play for artistic freedom.
I’ll confine myself to 10 American films since 1960:
(in random order)
Clerks
The Godfather
Psycho
This is Spinal Tap
Animal House
The Breakfast Club
Halloween
Rope
Jaws
A Clockwork Orange
Most of mine have already been mentioned, but their great movies
Rashomon
Yojimbo
The Godfather
The Good, The Bad, and The Ugly
The Jerk
Fight Club
12 Monkeys
Samurai Fiction
The Atomic Cafe
Raising Arizona
I wanted to thank eyeryone for their suggestions. There are some great movies listed here to get me started on my quest for movie mavendom.
Whisky Galore
M
Badlands
Goodbye Mr. Chips
Zulu
Chitty Chitty Bang Bang
Brief Encounter
A Matter Of Life And Death
The Battle Of Britain
This Is Spinal Tap
Natural Born Killers
Death Race 2000
Rebecca
Brighton Rock
A Clockwork Orange
Maths was never my strong point…
1. The Star Wars Series (Strictly no prequels)
2. The Indiana Jones Series
3. The Godfather Series
4. Dumb And Dumber
5. The Untouchables
6. Mackenna`s Gold
7. Bridge on the river Kwai
8. Top Gun
9. Terminator 2
10.Ben Hur
There’s too many to pick just ten. We should be able to do this by genre. 
And in no particular order…
~ Apocalypse Now
~ Frances
~ A Clockwork Orange
~ Harold and Maude
~ The Exorcist
~ The Godfather, Parts I & II
~ The Usual Suspects
~ You Can Count on Me
~ Pink Floyd’s The Wall
~ Magnolia
There’s also SO many honorable mentions, but the absolute most favorite of mine would have to go to Willy Wonka and the Chocolate Factory. Whee!
Harold & Maude
The Day the Earth Stood Still
Inside Daisy Clover
The Glass Menagerie
Leaving Norman
Fantasia
King of Hearts
Fantastic Planet
M.A.S.H (the movie)
The Hospital
I direct your attention to my personal version of the Good Stuff wherein you may pick any ten you like and you’ll be golden. There’s plenty of overlap with titles which have been listed before, but there are a few which may be unique to my list. Hope this helps.
Deep Throat
The Devil and Miss Jones
Behind the Green Door
I am Curious Yellow
Faster Pussycat Kill Kill
The Stud a.k.a. A Party at Kitty and Stud’s
Debbie Does Dallas
Inside Misty Beethoven
9 1/2 Weeks
A while back the American Film Institute released its Top 100 American-made films of all time: AFI Top 100
You might find it helpful in rounding out your collection. We’ve got it posted on the 'fridge and are slowly working our way through the list.
Here’s my picks (in no particular order):
Casablanca
Gone With The Wind
Wizard of Oz
Fantasia
Raising Arizona
Das Boot
Dances With Wolves
The Good, The Bad, And The Ugly
The Godfather
The Godfather Part 2
My honourable mention list would include stuff like Bull Durham, Jerry MaGuire, Star Wars, Star Trek II: The Wrath of Khan, Lawrence of Arabia, Psycho, This Is Spinal Tap, Crouching Tiger, Hidden Dragon, The Truman Show, The Princess Bride, The Terminator, Blade Runner, Blazing Saddles, Monty Python and the Holy Grail, etc…
Koyaanisqatsi
For All Mankind
Gladiator
Bladerunner
Patton
Star Trek II: The Wrath of Kahn (even if you’re not a Trekkie, you’ll enjoy the director’s commentary [he’s not a Trekkie either])
Henry and June
Crimes of Passion
Blackhawk Down
Apollo 13
1.) Casablanca
2.) M A S H
3.) Dr. Strangelove
4.) The Seventh Seal
5.) The Wizard of Oz
6.) The Year of Living Dangerously
6.) The Mask of Zorro
7.) It’s a Wonderful Life
8.) The Wicker Man
9.) Educating Rita
10.) Terminator 2
ok… here goes my picks…
Trainspotting
Instead of Casablanca , which I never liked (sorry), I love Alfred Hitchcocks *Notorious * with Ingrid Bergman & Cary Grant. Maybe its because Humphrey Bogart doesn’t really do it for me
Godfather- 1 & 2 never tired of those two movies
*Gone With the Wind
and
Star Wars- A New Hope and Empire Strikes Back
go without saying.
Just for Robert Duvall’s outstanding performance and the fact that its based on one of my favorite books of all time- despite being a tv movie:
Lonesome Dove
A Clockwork Orange - didn’t see this until a couple of years ago
*Persuasion * and Pride & Prejudice - the newer BBC versions.
Say Anything - the ultimate teen movie
Best in Show for laughs and because I’m a dog person and I get it.
The Princess Bride - for being truly original and great writing
ok… I can never keep it to 10…
Fear & Loathing in Las Vegas one of the few movies that stuck to the spirit of the book.
The Shining which wasn’t true to the book entirely but damn those creepy twins and Jack Nicholson- great shivers…
Requim for a Dream
Trainspotting
A Clock work orange (books is still better)
Amelie
My first Mister
Magnolia
Memento
I never promised you a Rose garden
Ocean’s 11
Pet sematary