Sliding Scale of Video Game Objectives

In any Video Game, your primary goal is to survive to the end. How much else you need to do between here and there, on the other hand, is entirely up to the game developer.

Objectives in a Video Game or Tabletop RPG may be described in a variable amount of detail; the variety of such specificity goes along a sliding scale thusly:

Win - The most basic type of Objective, this is when the only objective is to survive the level to the end. Since "Win" is the basic goal of every game ever, that makes it essentially a Metagame.
 * Doom -- just run through the game, shooting anything that gets in your way, and reach the exit.
 * of course, sports or fighting games
 * Flower on PlayStation 3. Although since you can't die, it's really only "reach the end of the level."

Broad - One step up from "Win", this is a mission objective which is so broad in scope or definition that it may seem to lose all practical meaning. For more recent games, this is usually tempered by morphing into a Sequential Objective; in most cases, you may have to accomplish specific tasks in order to proceed, but these will not be listed as actual Objectives.
 * Jedi Outcast had mission objectives like "Investigate the Outpost". Ooooooooookay. There were usually specific tasks you had to accomplish, but you had to figure out for yourself exactly what those tasks might be.
 * Myst literally drops you into a new universe without any instructions whatsoever. Exile and Uru (from later in the story) function in much the same way.
 * Some sports games might fall into this, if you're in a "league" and your orverarching goal is some kind of tournament; your base objective is still "Win".
 * Boss Battles would probably fall under this tent.
 * FIND STRELOK. KILL STRELOK.

Task-Based - The game actually gives the player something to do, and tells you what to do (though usually not how to do it). These can typically be fulfilled in any order, unlike Sequential Objectives, but failure of any one Objective usually results in a Nonstandard Game Over.
 * Golden Eye 1997
 * Perfect Dark
 * Syphon Filter
 * Riven (the sequel to Myst) falls in this category ("Find Katherine, capture Gehn using this book, signal Atrus"). So does Revelation ("Keep an eye on Yeesha"), although in this case the instructions are not only vague but actively misleading...
 * The SNES version of Alien 3.

Sequential - Related to Task-Based, Sequential Objectives are, as the name implies, a series of tasks in which one action leads directly to the next, or a given task may not be possible until certain other tasks are completed. Some games try to hide the sequential nature of the Objectives by having newer Objectives appear only after previous tasks have been fulfilled. Often a sign of a Pinball Protagonist.
 * Some of the objectives in Perfect Dark
 * Most James Bond-inspired games following Golden Eye 1997 take the "sequentially revealed objectives" route.
 * So does Star Wars Battlefront 2
 * The Dark Forces Saga managed to sneak these into certain levels.
 * Revenge Of The Sith features specific objectives which pop up at just the moment you need to accomplish them.
 * Supreme Commander combines this with a "sequential map". As objectives are completed, new ones will appear in an area of map that is suddenly made available that the player could not see before.
 * The Splinter Cell series regularly had objectives that didn't show up until you completed other, earlier objectives, combined with objectives that didn't occur until something happened in the world outside of your mission, which your Mission Control reacted to.
 * Halo.
 * Dead Space. "Thanks for fixing X, Isaac, but now Y is broken! Fix it!"
 * The Assault gamemode of Unreal Tournament is based around a mixture of this and Win: the attackers have to accomplish several objectives in the specified order to win while the defenders merely have to hold them off until time's up. Then the roles are reversed and the former defenders have to beat the time of the former attackers and/or (in UT2004) accomplish more objectives than the former attackers.

Quest - Standard in RPGs. There is one large overarching goal (other than "Win", that is), and several sub-quests, which may or may not directly relate to the Quest at first glance; or, the overarching Objective may be split into several "tasks". Quest-style Objectives, especially sub-quests/tasks, often overlap with Sequential Objectives.
 * of course, RPGs
 * Tron 2.0
 * Deus Ex

Optional - again, Exactly What It Says on the Tin. These are objectives which will prove worthwhile in the end, but are not game breakers if they are not achieved. They can fall into any of the categories listed above.
 * Project: Snowblind
 * Perfect Dark Zero
 * Fallout 2 was notable because almost the entire game was optional. If you could avoid having your level 2 Chosen One's head squished like a grape from the enemies you find there, you can go straight from the tutorial level to the Enclave bases.
 * In Arma 2, objectives will present themselves in missions and you can choose right then and there to accept or ignore them. Completing them effects how the campaign does overall, especially in regards to the disposition of the locals.
 * Each level in Painkiller has an optional sub-objective specific to that level, which rewards the player with a new card in the Black Tarot deck. These objectives generally range from weapon restrictions (beat the level using only the Painkiller or the Stake Gun) to combat challenges (beat the level while keeping your HP above 50, or don't collect any armor in the level) to fetch quests (find every ammo drop or secret in the level).
 * Yume Nikki does have objectives (which can be done in almost any order) and an ending, but these are basically incidental to the game's true appeal: wandering around aimlessly through the protagonist's creepy, depressing dream world.

This trope can also show up in other media, normally in a Mission Briefing.

For those that cannot be won at all, see Kobayashi Mario.