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Oh there are some good choices, for the most intense 10 minutes of film ever my vote would have to be the Russian Roulette scene in The Deer Hunter.

Of course there is also C'était un Rendezvous... which should get special mention in this thread as the entire film is under 10 mins. ;) It has no dialogue or cheesy sound track; it's simply a camera strapped to the hood of a Ferrari going through the streets of Paris as fast as it can.
 
The first 10 minutes of the movie "Red Dawn".

Yeah, it's an awful old Patrick Swayze movie, but the opening scene is just wicked. ;)
 
Either the first or last 10 minutes to Leon. I mean the middle bit is fantastic too but the start and end are really concentrated moments of character and story.

I'd have to go with the last 10. The first 10 is good character development, but only in one dimension. Someone watching the last 10 would see developed that dimension, as well as the rest of his personality. Astounding work, even if none of my friend's appreciate it.
 
The Vince and Jules scene from Pulp Fiction with Brett and his friends. Pure class. You know from the moment Samuel L Jackson starts talking that they're all dead.

Jules Winnfield said:
And I will strike down upon thee with great vengeance and furious anger those who would attempt to poison and destroy my brothers. And you will know my name is the Lord when I lay my vengeance upon thee!
 
The car chase scene in "Bullet"

I will also agree with the first ten minutes of "Saving Private Ryan".
Absolutely some of the most intense war reenactment ever.
 
My selections:

The naked fight scene in Eastern Promises in the steam bath-house.
Viggo Mortensen was bad-ass in that movie.

The opening scene in Saving Private Ryan. The best movie war scene I've ever scene on film.

There are many 10 minute clips from Apocalypse Now! that qualify. Here is one: the sequence when Martin Sheen is getting drunk in his hotel room and punches the mirror, and rubs his blood all over his face (during which he actually was getting drunk, actually did punch the mirror, and actually did cut his hand. It was his birthday, and after that scene he was rushed to the hospital with a mild heart attack. If you liked AN, you must rent Hearts of Darkness, which is a documentary of the making of AN.)

I also think that the sequence in the Matrix where Neo is given the pill choice, and he finally 'wakes up'. I wish I could go back and watch that with virgin eyes again.

In Empire Strikes Back- the Luke vs. Darth Vader lightsaber fight after which he finds out who his father is.
 
The section of Fight Club where Edward Norton's character makes his realization about Brad Pitt's character. I would give more details, but it's a pivotal part of the film/book, and I don't want to ruin it for people. :)

Ha! That book/movie is pretty old now, if they haven't seen it by now, you're probably not ruining much ;)

Do all of Val Kilmer's lines as Doc Holliday in "Tombstone" add up to around 10 minutes? I love that movie! :D

"You're a daisy if you do"
 
One that always sticks in my mind is the scene in The Royal Tenenbaums where the Luke Wilson character cuts off his hair and beard and then cuts his wrists, while 'Needle in the Hay' by Elliott Smith plays. Not exactly 10 minutes, but powerful nonetheless.
 
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