How do you write an opening scene or sequence that makes the viewer want to keep watching past the first few minutes? This is a question that has haunted me for as long as I have been writing screenplays. The first rule of screenwriting is as important as the first rule of Fight Club: show don't tell.
So in my screenplays I try to show something about the lead characters that would potentially surprise or not fit the expectations of the audience. I am going to reference three show stopping opening scenes from film and TV to indicate how they kept me interested in learning more. 
The first is the Breaking Bad pilot's opening sequence with Bryan Cranston in his underwear. This sequence, written by Vince Gilligan, is considered iconic for good reason.
We see the pants flying in the air as the first frame of the pilot and we are intrigued. Who is the owner of these pants? Two men wearing gas masks careen through the desert in a Winnebago that has assuredly seen brighter days. Who are these people? Walter White we learn is a family man who as he hears the police sirens seemingly narrowing in on his location, leaves a last will and testament of sorts for his beloved family. This is someone we want to get to know better. This is a hero of our times.
Another TV pilot that still has screenwriters talking is the pilot for J.J. Abram's Lost. This particular pilot is cinematic in its scope and ambition. A plane crashes on a beach on some unknown shore. People who were strangers are charged with becoming brave, braver than they've ever been in their whole lives. The pilot script describes the scene as like a "warzone" with "scattered fires and wreckage" everywhere. This is a maelstrom of death and destruction.
This is a scene of absolute carnage, and we are thrust right in the middle of it with Jack, Matthew Fox's character guiding the way. There are dozens of people milling about trying to salvage something, anything in the chaos. This pilot, written by J.J. Abrams and Damon Lindelof, had a budget of between $10 and $14 million - the most expensive pilot episode at that time... and it shows. Every dollar is portrayed onscreen to dizzying effect.
Even though there are dozens of people on the beach, the pilot does center us around a main character of sorts. And that is Jack: our hero who immediately saves the cat so to speak by helping the people around him who are all in some kind of danger or abject misery. This focus on a main character - a main hero - even in an ensemble cast is an important aspect of crafting a killer opening scene or sequence.
Next up...Drive. Ryan Gosling's unnamed character says very little in the opening scene and in doing so, communicates a lot. His reticence leaves us to focus on what he is doing. The roar of his 300-horsepower Chevy Impala and Bryan Cranston's one-sided pep talk stand out in the face of Driver's silence. His silence also highlights what he does in fact choose to say when we first meet him: "You give me a time and a place. I give you a five minute window. Those five minutes, I'm yours...Minute either side you're on your own."
Drive is a film with a distinct style. The jacket Driver wears, the sound design, the nighttime cityscape of Los Angeles. These all seek to build a neo-noir arthouse vibe that wouldn't be out of place in a European film. Nicolas Winding Refn's film is just plain cool and so is Ryan Gosling's character.  
What Drive has in common with Lost and Breaking Bad is a distinct sense of time and place and a strong lead character with a certain magnetism. In the case of Breaking Bad, the viewer feels they are in that Winnebago with Walter White. It would be hard to picture anyone else in the role of extra ordinary everyman. With Lost, the sight of that Lockheed 1011 torn to bits and pieces is immediately jarring and the spectacle of it all leaves you on the edge of your seat. Matthew Fox's Jack immediately distinguishes himself as a prototypical hero. 
Driver and Walter are both antiheroes. They are both living on the wrong side of the law when we first meet them. They are also both very sympathetic - Driver because he's a cool part-time Hollywood stuntman and Walter White because he's a suburban dad just trying to provide for his family. 

The key to a compelling opening scene is a captivating protagonist that the audience can relate to or look up to. Going big with cinematic special effects or story elements like a careening Winnebago in the desert or a getaway from an armed robbery fills the audience with anticipation. Starting in medias res and introducing the main character almost in the first frame sets the stage for a thrilling story with edge of your seat expectations. Having a magnetic lead doesn't hurt either.
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