I’d like to speak for the 80s mainstream and add Back to the Future and Ferris Bueller’s Day Off, both of which are paced to perfection and lots of fun to boot. Moving into the 90s I might suggest Groundhog Day.
Now I think of it, Whit Stillman’s Metropolitan is as close to perfect as I know. Jane Austen would be proud.
Honorable Mention: Michael Verhoeven’s The Nasty Girl (is it necessary to be German, or have one in your family, to enjoy this? I love it. Please advise).
The Iron Giant was flawless. Perhaps I’m biased because as a youngster I would lay awake at night dreaming of my own giant robot friend. Brilliant casting for the voice actors too. Say what you will of him but nobody could have done the voice of the robot better than Vin Diesel.
I would like also to throw out another vote for O Brother, Where Art Thou.
I don’t care what anybody says, I simply loved Being John Malkovich Don’t know quite what genre to put this into…psychocomedy?
2001 A Space Odyssey - Probably the best Scifi that has been or will ever be made. A testament to what obsession can accomplish (read about Kubrick’s maddening struggle to finish this film), and light-years ahead of its time in concept.
The Godfather - The gangster flick that broke the mold. Never equalled. Marlon Brando’s Don Corleone will be rememberd as one of cinema’s strongest characterizations, ever.
Taxi Driver - Probably De Niro’s finest role, and surely the best noir, urban psychodrama in history. Then again, maybe De Niro’s best was Raging Bull…both damn good.
The Pianist - For best war film. Say what you will about Roman Polanski, this film is a masterpiece.
Le Fabuleux Destin d’Amelie Poulain - For best romance. Best date movie ever made, IMO!
The Silence of the Lambs - For best thriller/horror flick. Hopkin’s Hannibal Lechter is, hands down, the finest baddie ever seen on screen.
The Good, the Bad, and the Ugly - For best Western (albeit, the Spaghetti variety) I see this flick once every year, and never tire of it. Eastwood had it all over the other so-called cowboys. And Enio Moricone’s soundtrack is simply the outstanding classic of the genre.
** Casablanca ** is amazing because it’s like every single line in the movie completely works. My husband and I saw years ago and were delighted to find out the source of all the Bugs Bunny cartoons. 
** Toy Story ** is not only great but the one of the few films where the sequel is just as good as the original.
** Singing in the Rain ** would be perfect if they would eliminate the dance sequence with Cyd Charise. It’s too long. But I love it anyway.
I second 2001: A Space Odyssey and Toy Story (or whatever the count is at).
Johnny Depp agrees with you.
He’s also a big fan of Jim Jarmusch* and Tim Burton (of course).
*Speaking of, one of the cable stations has been running Mystery Train a lot lately.
La Haine
Spirited Away
Belville Rendevous
City of God
Goodbye Lenin
Strangley I have seen all of these films in the last two weeks and they are absolutley amazing! I urge you to see these NOW.
I’m astonished by the extremely generous assessment of perfection that so many of you are giving. Ichi the Killer??? Wow.
This is the only one that bugs me, though, because the flaw is glaring and very nearly ruins the film: the over-the-top (and false) pure Spielbergian inability to let the story tell itself honestly ending where Schindler gets all weepy and guilty. Never happened, cheapened the film.
2001: A Space Odyssey
A Clockwork Orange
Pulp Fiction
Fight Club
The Lion King and Nightmare Before Christmas? It’s been a very long time since I’ve seen these, but I can’t remember any flaws in either.
I thought Spielberg could have retired after that movie it was so nearly perfect. It personified the Holocaust in a way that simply isn’t likely to be surpassed.
The alternative would have been to let Mr. & Mrs. Schindler just leave as they did in real life (accompanied by two of the Schindlerjuden), which was done strictly because they were on the lam. While more realistic it would have been very anticlimactic, and while he didn’t give a speech about it at the time Schindler was, according to the surviving Schindlerjuden, tortured by the thoughts that he could have saved more. So, while I’m aware of the true story I thought this one worked better for film without betraying the integrity of the tale.
I remember an interview with Winona Ryder around the time Schindler’s List came out, incidentally, in which she was mentioning her work with Martin Scorcese and remarked “If Martin had made Schindler’s List it would have taken place in the 1960s and 1970s and been the story of a man sponging off the Jews he saved in the Holocaust.” Interesting concept.
Another loosely adapted B&W biopic that I’d enter into flawless films:
Ed Wood
Agree wholeheartedly with To Kill a Mockingbird, The Philadelphia Story, and The Godfather.
Would add:
American Beauty - incredible cinematography
The Princess Bride - “by S. Morgenstern. Chapter one …”
From reading this list, perfection is clearly in the eye of the beholder. 
When I was ten I thought The Golden Voyage of Sinbad was the perfect movie: after all, it was practically nonstop Ray Harryhausen monsters and it had none of that mushy character development stuff found in grownup movies. And what could be better than that?
Somehow I don’t think what I believe is perfect at 40 is any significant degree closer to the ideal of perfection than what I thought at ten, so I’ll stick with that.
I agree with tons of ones alread mentioned but I’l throw in a few original ones.
**
Groundhog Day
Trainspotting
Iron Giant
Evil Dead II
Raising Arizona
The Apartment
When Harry Met Sally
Manhattan
Star Wars IV & V**
and less acclaimed but a personal favorite:
Beautiful Girls
Gods and Monsters
I too think that a lot of the movies mentioned are truly GREAT movies, but are not perfect. “Schindler’s List” is a truly wonderful, magnificent film, but it’s not perfect - it does have some flaws. As lissener points out, you can have a film with significant flaws be better than a film with no flaws. It’s like having a ballplayer with no weakness who’s good at everything, and another player who isn’t very good at stealing bases but hits 50 homers a year so he’s better overall than the guy with no weakness.
In my entire life I’ve seen four perfect films that were also GREAT films, films in which I could detect not a single thing wrong but almost everything was really good:
To Kill a Mockingbird
Toy Story
Back To The Future
The Godfather
That’s it.
I have to disagree wholeheartedly with Gangs of New York. That movie was the biggest waste of three hours I have ever spent in my life. Why go to a movie and care about these characters to find the ending trumps all conflict? It’s the most anticlimactic movie I have ever seen.
I have yet to see a movie that I would say is “perfect.” The only movie I can think of that conjured thoughts of perfection immediately after seeing it was Eternal Sunshine of a Spotless Mind. Of course, I’ve seen it only once and I would have to see how it withstands multiple, less emotional, and more critical viewings.
My problem with GoNY was actually that I didn’t care about any of the characters. Bill the Butcher was a fascinating fellow, but he certainly deserved to die, and DiCaprio’s character didn’t have enough character development to greatly provoke any caring. As for the in-way-over-her-pretty-little-head Ms. Diaz, I started laughing so hard when I saw this Civil War era NYC immigrant street hustler lift up her blowse to reveal
a botched Caesarian scars over washboard abs
that I missed almost anything else she said or did.
That’s why I pointed out Gods and Monsters. It may not be more than a minor film, but I can’t think of a single aspect–acting, cinematography, lighting, directing, script–that could have been modified in any way to make it better than it was, for what it was. Whether one likes what it was is irrelevant; it is consummately crafted.
And I’ll say it, cinematic blasphemy that I know it to be: while I certainly enjoyed To Kill a Mockingbird, I’ve never really understood its Olympian status. It left out so many of the most wonderful portions of the book (particularly the “drunk” white man with the black “wife” and children, the children going to church with Calphurnia, Atticus’ sister, etc.) as well as the revelation that Mayella’s father forced her to submit to incest, a vital fact to understanding her character. I would love to see the movie remade as an HBO/Showtime miniseries (i.e. a cable company with a large budget and no censors). Strangely when I read the book I pictured John Lithgow as Atticus, Rue McLanahan as his sister and, of course, Whoopi Goldberg as Calpurnia, but any number of other talented actors could do the job.