Big First Choice

You escape the enemy's dreadnought aboard your commandeered shuttle, with the rescued rebel leader in tow and mere seconds to spare before the explosive charges you planted crack the monstrous ship in half. Not a bad job for the tutorial level. As the adrenaline wears off, the rebel leader congratulates you for your courage and offers you a chance to work alongside her to help free the galaxy from the Dark Order's clutches. But your hero would have to give up his grand life as a space mercenary, an outlaw-for-hire: certainly he's no friend of the Order, and he's more than happy to fight them on his own time, but he chafes at taking orders from anyone.

You ponder the decision for a few seconds, then have your hero turn down the offer with characteristic nonchalance. You then spend the next twenty hours of this epic space opera being inadvertently dragged into one conflict after another, meeting the rebels under awkward circumstances, and generally making life hell for the Order. Finally, when all's said and done, you get to put a bullet between the eyes of the Shadow Prince, collect your reward and fly off into the sunset.

Feeling good about your victory, you go online to discuss the game. But what's this? You don't remember an infiltration mission aboard a satellite. And a romantic subplot with the rebel leader? How come no one's talking about the MX-6000 railgun that got you through the final stages, but they're all gushing over that multi-missile launcher that the Elite Mooks had towards the end? Certainly you don't remember getting one.

After skimming a few threads, you can't help but wonder: did you even play the same game as everyone else?

The answer: not quite. As it turned out, a lot more was riding on that innocuous first question than you ever could have guessed. By making one choice or the other, you determined the entire course of the rest of the game.

Not every game is quite as extreme as this example, but the Big First Choice (or second, or third) is a common way of extending the life of a game by making the player's choices at key points have a dramatic effect on the way the game plays out - perhaps even the way the game plays, period. Multiple playthroughs are absolutely necessary to wring One Hundred Percent Completion out of games that feature such choices: sometimes the different paths will converge again at the end, but it's just as likely that each individual choice will lead to a different ending.

Examples of Big First Choice include:

Action RPG

The first thing you do in Nox is pick your Character Class, which also decides which one of three largely different storylines the game will follow.
Played with and Lampshaded in Super Paper Mario. Your first choice of the game is whether you will accept the challenge of saving the world. If you say no three times, you don't save the world and automatically get a Game Over.

Adventure Game

At about the end of the first third of Indiana Jones and the Fate of Atlantis, the game splits into one of three possible paths depending the player's choice: the combat-centric "action" path, the self-explanatory "puzzle" path, or the "team" path where Indy travels together with Sophia. These paths all converge at the last act in Atlantis, and beating all of them is required for the maximum Indy Quotient points.
In the Adventure scenario of Clonk's "Metal and Magic" pack, you can either choose becoming a mage or a paladin, and both choices lead to quite a long story...or you can become a roadsweeper, which ends the story in about five minutes.

Eastern RPG

Kingdom Hearts and its sequel ask the player to choose which skills to emphasize and de-emphasize (strength, magic or defense) and how quickly they level up at the start of the game. Woe to the player who might unknowingly choose to level up slowly at the start.
In Final Fantasy X-2, at the beginning of Chapter 2, you have to decide which of two factions to give an important MacGuffin to. This affects which faction-related sidequests will be available to you later.
In the Pokémon series, your choice of starter Pokémon determines your rival's starter as well: if you choose the Grass-Type starter, he'll choose the Fire-Type; the Fire-Type starter, the Water-Type; and the Water-Type starter, the Grass-Type (i.e. whichever you choose, he gets the one that's strong against it). Yellow is an exception: there, your starter is always the Electric-Type Pikachu, and your rival's Eevee will evolve into Vaporeon (weak against Electric), Flareon (neutral against Electric), or Jolteon (strong against Electric) depending on how often you lose to him. Your rival's starter (or his starter's final form) will also determine his final team.
- Also, in the FireRed and LeafGreen remakes, your choice of starter determines which of the Legendary Beasts from Generation 2 will roam the Kanto region: choosing Charmander will cause Suicune to appear, choosing Bulbasaur will cause Entei to appear, and choosing Squirtle will cause Raikou to appear.
In Radiant Historia, one of your earliest decisions is whether to stay with Heiss in Special Intelligence, or join your friend Rosch in his new brigade. Due to the nat ure of the game, of course, the paths are not truly mutually exclusive, and because of some interplay between the two diverging timelines, it is not only possible but necessary to experience both.
In Radiata Stories, you have to decide whether to stick with the humans, or join the Elves. The decision changes the entire second half of the game.
Front Mission 3 has quite possibly the most extreme example in all of gaming: an innocuous choice at the beginning (whether or not you want to hang out with an NPC for drinks) determines your entire path through the game. There are two complete storylines with wildly different results throughout, all hinging on that little choice.

Stealth Based Game

At the start of Metal Gear Solid 3: Snake Eater, the player will be asked to choose their favourite game in the series. Picking Metal Gear Solid makes Snake's stamina decrease more slowly; picking Metal Gear Solid 2: Sons of Liberty starts the player wearing the Raikov mask in the very first cutscene; and picking Metal Gear Solid 3: Snake Eater unlocks a "Peep Theatre" cutscene.
In The Nameless Mod, after leaving the starting area, the player has the option to join either PDX or World Corp. It affects the entire plot of the game, most of the missions, and even which locations you encounter.

Survival Horror

In the first chapter of Eternal Darkness, you have to pick up one of three artifacts. Which one you take determines which of the three Ancients will be the Big Bad of your playthrough, which also affects which of three attributes (Health, Magick, and Sanity) the protagonists are particularly strong/weak in.
A decision made early in Saw II: Flesh and Blood determines who survives at the end of the game.

Visual Novel

Visual Novels as a genre tend to have this at their core, especially if they have multiple largely independent storylines branching off early in the story, depending on a few innocuous choices early on.
In Tsukihime, a few less than obvious choices during the first two days of the story determine which one of five branches it will follow for the rest of it. It doesn't help that some options and branches only become available after you clear other endings.
In Fate Stay Night, you are given a few choices regarding how you follow your day as an Ordinary High School Student... and the answers you give determine which route you follow for the rest of the game.

Western RPG

Dragon Age: Origins has its eponymous Origin stories: class/race-specific pseudo-tutorial misssions, the consequences of which come up again and again throughout the rest of the story.
In Sid Meier's Pirates!, your choice of nationality and era determines your starting ship, crew, and home port. The era chosen also determines the balance of power among the four nations on the game map. You are also given a choice of one of four different skills, each of which make a different aspect of the game easier to manage.
An early quest in Fallout 3 gives you the choice of blowing up the city of Megaton by setting off its namesake bomb or working to disarm it permanently. Setting off the bomb is a good Start of Darkness for an evil character, as it "rewards" you with a serious hit to your Karma Meter.