You’re right, OrcaChow. brachy shouldn’t post with dead brain, and…
Children Shouldn’t Play With Dead Things.
It’s A Mad, Mad, Mad, Mad World.
Dead Men Don’t Wear Plaid.
The Corn Is Green
The Best Little Whorehouse in Texas
Paint Your Wagon (You is implied)
Does Zorro, the Gay Blade count?
Ernest Needs A Kidney
White Men Can’t Hump
You’ve Got Male
I’ll Do Anyone
What About Boob?
Inspect Her Gadget
Wet Dreams May Cum
Honey, I Shrunk Your Clit
Play it to the Boner
I Know What You Did Up The Bummer
There’s Something In and Out of Mary
Diddle-her on the Roof
Spray it Forward
I’m pretty sure none of these are repeats.
I’ve never seen the movie, but my friend and I invariably show it to one another every time we go into the video store. Hilarity ensues. 
This is not a sentence.
Surreal and bizarre, this is one of my favorite “strange” movies.
How about, Tie me up! Tie me down!
Since when does a sentence have to have an object? Don’t you all remember junior high English class. Take, for example, “My car runs well.” It is a complete subject, but lacks an object. Also, imperative sentences obviously qualify, even though they don’t necessarily have stated subjects. The shortest title that could therefore qualify would be Go, depending on whether or not you take it as a command.
How Green was my Valley indeed is a sentence, if you take it is a question. How the Grinch Stole Christmas is not. It has a subject and verb, sure, which qualifies it as a clause, not a sentence. A sentence must be an independent clause, while the word “How” in that title makes it a dependent clause.
And for my contribution:
What’s Eating Gilbert Grape?
And who could forget
[ul][li]Don’t Be a Menace to South Central While Drinking Your Juice in the Hood[/ul][/li]May I hijack this (somewhat) and ask about T.V. shows?
[ul][li]Are You Being Served?[/li][li]Parker Lewis Can’t Lose[/li][li]Joanie Loves Chachi[/li]Who’s the Boss?[/ul]
I don’t think anybody believes a complete sentence has to have an object, that is just the way the rules for this little exercise were put forward by Danimal.
Though really, if we don’t insist on an explicit subject, verb, and object I don’t think such titles would be rare at all.
scratch, I tried Don’t Be a Menace to South Central While Drinking Your Juice in the Hood earlier and it was correctly pointed out that the subject in implied.
I’ve seen this movie! From 1972, and I believe the Bob Clark who directed later directed Porky’s and A Christmas Story!
Damit, Danimal, you beat me to it. In the same breath I was going to mention my favorite anti-Grateful Dead song,
Bring Me The Head Of Jerry Garcia
Nothing wrong with an implied subject as far as I (and any grammarian) is concerned. If I say “Stop!” that’s a sentence, short as it may be. 
My submission: Mom and Dad Save the World (1992)
Again, it isn’t that an implied subject or an absent object do not make for complete sentences, it is just that they don’t fit the sentence structure requested in the original post.
I Want To Live!
You Can Count On Me
I Never Sang For My Father
You’ll Never Get Rich
Men Are Such Fools
A Lion Is In The Streets
You Can’t Get Away With Murder
Guess Who’s Coming To Dinner
She Wore A Yellow Ribbon
Life is Beautiful
The Englishman Who Went Up A Hill And Came Down A Mountain
I Come In Peace
A Fish Called Wanda (?)
Wanda and Hill/Mountain have no verbs. Nice phrases, though.
Get Carter
I Confess
It all depends on how far you’re willing to stretch reality. Perhaps there was a fish who SUMMONED Wanda. A fish called Wanda. Wanda replied “yes, my love?”
The Englishman Who Went Up A Hill And Came Down A Mountain.
Perhaps Who was the guy’s name, as in: The Englishman Benny Hill Went Up A Hill And Came Down A Mountain.
Perhaps I should take a nap.
(disclaimer: the above post is a feeble attempt at humor, and even though I can see I failed miserably, I’m posting it anyway just because. Don’t correct me, because idiocy is the whole intent of the post: I know it’s incorrect)
Creative, very creative. Enjoy the nap.