To Kill a Mockingbird is the best.
others that come close…
Oscar
Die Hard
Murphy’s Romance
Phillidelphia Story
I agree with a number of films mentioned (disagree markedly with a couple) but would add:
**The Maltese Falcon
The Longest Day
The Philadelphia Story** and its musical remake High Society.
For my honorable mention I would suggest We’re No Angels (the one with Bogart, Ustinov and Rey) The Pink Panther, Day of the Jackel and Topkapi.
TV
Day of the Jackel (the original of course) is a great choice. When you find out what the story is about, you know he doesn’t succeed because it’s in the past. So how the hell can it be exciting? But it is, time and time again.
Another vote for Amadeus. Simply one of the finest movies ever made.
I’d also like to nominate Branagh’s Henry V. The only movie I’ve ever gone to see four times in the theater.
And nobody has yet added Young Frankenstein to the list? Shocking.
Jaws
Annie Hall
Could this movie get better? I don’t dig the genre but this is a really enjoyable film, the characters are deeply developed and the humor is outstanding. Possibly flawless??
Joeski said Pulp Fiction, yeah to that.
The Producers?
Little Big Man- perfect cast, perfect story
Richard III (the Ian McKellen “1930s fascist alterniverse” version)
Schindler’s List (although sometimes I wonder if it would have been better in color since the BW gives it a documentary look that distances us)
Roger & Me I’ve come to loathe Michael Moore, but that movie was brilliant
1776 (now that Cool Considerate Men has been restored)
Badlands may not be my favourite movie of all time, but it fit together so perfetly. Except for some of the music (not the Carl Orff bits, those were great. That other, really grating organ- or something, electric flute?- music that plagues most 70s movies, playing while they’re driving). Damn. Still seeking perfection…
Does Girls Gone Wild: VII count as a film? Or Dorf on Weightlifting?
Adding my voice to the mentions of To Kill a Mockingbird, 1776 and Casablanca.
But a few other movies I consider flawless aren’t mentioned here yet:
All About Eve
All the President’s Men
A Christmas Carol (1951 version w/Alistair Sim)
Rebecca (1939)
Tootsie
A Tree Grows in Brooklyn (original w/Peggy Ann Garner & James Dunn)
I can’t think of anything to improve in the above films, except perhaps that in every case I want them to last longer than they do.
(Anyone else think it’d be interesting to see a list of “Films that would be flawless if it weren’t for one thing…”?)
Another vote for Casablanca. And Death on the Nile with the late Sir Peter Ustinov. I’ll also offer Kind Hearts and Coronets. Of more modern films, how about The Mummy or Raiders of the Lost Ark?
O Brother, Where Art Thou
Rushmore
That Touch of Mink
Panic Room
Ghostbusters
Willie Wonka and the Chocolate Factory
Amadeus
Die Hard
Not necessarily the greatest films ever but they were all perfect for what they purported to be.
I can’t believe I didn’t think of this earlier…This Is Spinal Tap. Utterly hilarious and convincing. Somehow everything in that movie makes me laugh, from the token “these go up to eleven” and “none more black” lines to more minute things…like Ian’s expression when Fran Drescher’s character tells him that “money talks and [expletive] walks.” Priceless.
Also, The Emperor’s New Groove. Probably my favorite animated movie behind Toy Story…I think it’s the one movie I’ve seen that’s mastered sarcastic humor. Offhand I can’t think of a single line or joke that goes awry. I mean, even David Spade is great!
More recent: Hero (it’s being released in north america very soon, too.) That is truly a flawless movie.
Brother
The Blade
Ichi the Killer
ok, I have a thing for asian productions… but these are all amazing movies.
Brotherhood of the Wolf was excellent
La Femme Nikita was brilliant.
I hear they make some good movies in hollywood, too. 
-n
The Lion in Winter
Animal Crackers
Moscow Does Not Believe in Tears
High Fidelity. Not one forced moment, a perfect soundtrack, and the casting choices were all dead-on.
I’m ready for the flames!! 'Gangs of New York ’ is one of the best acted movies I’ve ever seen. I used to be a HUGE un-fan of DiCapprio also. GONY changed things a bit for me though.
I’ve got a fairly eclectic list:
Amelie
The Maltese Falcon
Ruthless People
Emma (1996)
*Miracle on 34th Street *(1947, of course)
The Day of the Jackal
And we can’t forget Lubitsch:
Trouble in Paradise
The Shop Around the Corner
Ninotchka