For me it’s “Cliffhanger”. I still remember the first time I watched it. Sitting on the couch eating a sub sandwich and settling in for the movie. It turned intense so fast and that scene stayed with me for a very long time. I rented it so I was able to pause the movie and I remember just sitting there and saying OMG OMG OMG OMG !
So many good films listed already, but let’s stray away from the classics. I like the start of “Pineapple Express”. The army officer tries in vain to get Pvt Miller to give straight answers when he is smoking “Item 9”. He gives up and commands, “Shut it down, bury this place, sell the land and get rid of him…” Off camera you hear a gunshot and the officer leans right into the camera, “ILLEGAAAAAAL!”
Dennis
I’m going to second Wall-E. It was a decent enough movie once the speaking characters showed up, but the speechless part was just breathtaking.
John Frankenheimer’s 1966 movie Grand Prix.
The shots of the Formula 1 cars revving and the use of checkerboard type editing. My favourite 15 minutes of any movie, they just happen to come at the beginning.
For the first 30 seconds of a film, how about “Gran Prix”? The screen opens to complete darkness, then the edges of a circle appear at the far reaches of the screen. As the dark circle gets smaller, then finally gets a bit of light inside, you can see it is the inside of an exhaust pipe and the camera is pulling away. Just as you figure that out, “BRAAACK!”, the engine starts.
I saw this in the original CinemaScope with surround sound and it was awesome.
Denis
Conan the Barbarian
The opening sequence that chronicles the destruction of his family is extremely good.
Sets the tone for the whole movie.
Was this brought up already in the thread?
Anyway totally agree on the gum chewing machine guy talking about a spherical object not part of the car. And the “you ate sand?!” scene. There’s so much comedy, nuance and story in those first 15 mins, I think I catch something new each time.
“Turn to the right.”
I was the fourth person that I saw that mentioned Raising Arizona’s first 15 minutes. I just mentioned some of the reasons I like it.
I realize it’s been a couple of months, but the opening was a rather disjointed montage of scenes played in slow motion that were similar to, but not exactly like, scenes that would transpire in the movie, all set to Wagner.
Butch Cassidy and the Sundance Kid
“Sundance, how good are you?”
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Another great opening credits rather than opening scene. The Big Easy was a mediocre corrupt cop movie, but the opening credits had fantastic visuals of a low level flight over the coast and bayous around New Orleans.
Oh man, I forgot about that. You’re right- it definitely does. Out of curiosity, when is the first 15 minutes up- when Conan’s master strikes off his chains and turns him loose? Or is it earlier than that?
Ninja’d you by 2 minutes. 
WINGS OF DESIRE
There is even a few seconds of Tuxedo Moon.
Oh yeah. One of the best. As is Pulp Fiction.
I’ll give a shout out to Dog Soldiers. Very calm… a training mission, and then WEREWOLVES.
Isthar. And I mean that seriously – the opening sequence is black comedy gold.
The opening to X-MEN is kind of crazy when you stop to think about it: yeah, you came in for a comic-book movie back when that didn’t mean what it means now, but after a little portentous Patrick Stewart narration we open up at a concentration camp where Jews are somberly getting herded to their fates in the rain, and, wait, what? They’re playing this absolutely straight? I expected a comic-book movie to start somewhere on the low end of a scale from one to ten, and it just begins at eleven?
Could’ve gone wrong – but they were looking to set a tone, and they pulled it off.
Did I miss it, or has no one mentioned Gladiator?
I also like Dances with Wolves, although contrary to the OP, I usually skip the first 15 minutes and jump to the part where he’s out west.
X-2was a pretty crappy comic book movie overall, but the opening three-minute sequence with Nightcrawler invading the White House and attacking the President, all claws and teeth and devil-tail and BOMFing (teleporting in a puff of black smoke) from one point to another, really hit all my spots.
Oh, yeah, and the pre-credit sequence from Raising Arizona was great! Anybody mention that yet?