Co-Op Multiplayer

"TRY TWO PLAYERS * MORE ENERGY * MORE COINS * MORE STRATEGIES * DOUBLE FIREPOWER * PLAYERS CANNOT HURT EACH OTHER"

- Xybots

There are several distinct types of Multiplayer modes in Video Games. This trope is a Sister Trope of Competitive Multiplayer, Meta Multiplayer and Massively Multiplayer.

Co-Operative
All players are on the same team, playing against the computer; this only counts if it's the “main game” and not multiplayer with the teams set to be players vs. CPU. The characters played by additional players are almost always Canon Foreigners, rarely making it past Road Cones. Comes in several flavors:

Individual
All characters have an equal amount of influence over the game itself, including camera control if it's a shared screen. Occasionally allows players to attack each other in some way, either for added difficulty or possible competition/hilarity between players, and may keep track of scores as well.

Examples:

Action Adventure

 * The Legend of Zelda Four Swords Adventures

Action RPG

 * Final Fantasy Crystal Chronicles

Beat Em Ups

 * The Battletoads console games all had two-player co-op. Battlemaniacs and Battletoads and Double Dragon offered players the option of not being able to hurt each other; the original game did not. The Battletoads Arcade Game was designed primarily for three-player co-op.
 * Double Dragon
 * Final Fight (with the notable exception of the SNES version)
 * Golden Axe
 * Knights of the Round
 * Dungeons and Dragons Shadow Over Mystara
 * The Simpsons
 * Teenage Mutant Ninja Turtles the Arcade Game
 * X-Men

First-Person Shooters

 * The Doom and Quake series, excluding the last (Single-player focused) games.
 * Heretic and Hexen naturally follow along, using the same engines.
 * EYE Divine Cybermancy
 * Halo: CE, 2 & ODST
 * Left 4 Dead
 * Marathon 2 & ∞
 * The Xbox port of Return to Castle Wolfenstein
 * Serious Sam
 * Unreal Tournament III's Campaign Mode.
 * Modern Warfare 2/3's Campain missions are cut and made into "Spec Ops" Missions
 * Splinter Cell Since the third game onwards.
 * Borderlands

Maze Game

 * Wizard of Wor, which in the arcade version also forced single players to contend with a computer-controlled ally's friendly fire.

Platform Games

 * Chip 'n Dale Rescue Rangers
 * Doom Troopers
 * New Super Mario Bros Wii
 * Sonic Colors
 * Rayman Origins
 * World of Illusion: Mickey and Donald really do help each other out in the co-op mode, which includes some levels not available to either character alone.

Real Time Strategy

 * Pikmin 2
 * Command & Conquer: Red Alert 3

Rhythm Games

 * Guitar Hero
 * Rock Band

Shoot Em Ups

 * Most 1942 games
 * Aero Fighters
 * Radiant Silvergun
 * Raiden
 * R-Type
 * Smash TV
 * Twinbee
 * Thwaite: In a single-player game, the player can fire from either of two missile silos with the two buttons on a controller or mouse. In 2-player, each player has his own cursor and can fire from one of the silos.

Western RPGs

 * Baldur's Gate
 * Diablo
 * Icewind Dale
 * Neverwinter Nights

Unsorted/Miscellaneous

 * Gauntlet (1985 video game)
 * Mario Bros.
 * Battle City
 * Warpman
 * Dungeon Siege
 * Glider
 * Nearly every Lego Adaptation Game.
 * Mario Kart Double Dash!!
 * Minecraft
 * Resident Evil Outbreak (until its servers were shut down)
 * Various single-player games like Rune, System Shock 2, Command & Conquer: Renegade and Unreal I have had their original campaigns superbly modded for coop MP by fans.
 * The Simpsons Game
 * World of Goo
 * Toejam and Earl
 * Heavy Weapon (the Xbox 360 version)
 * Splinter Cell Since the third game onwards.

Tag-along
One character is the designated “leader,” and has more influence over the game itself, particularly the focus of the camera. The other characters are optional and often expendable and may be controlled by the computer.

Examples:
 * In Dead Rising 2, the host player's progress through the story is used. The guest player starts with none of the items they have in their 1-player game, and when they leave they drop everything they're carrying. All the guest player keeps from co-op is any money and PP earned.
 * Death Spank
 * Demon's Souls
 * Dark Souls
 * Donkey Kong Country Returns plays this mostly straight, though Player 2 can continue the game by himself whenever Player 1 dies (as shown in this video).
 * Halo 3
 * In Madden NFL one player is responsible for calling plays. There is another variation with three players to a side, in which one player controls the quarterback and calls the plays, one player controls a running back, and the third controls a wide receiver.
 * Kirby Super Star and Kirby's Dreamland 3
 * Mercenaries 2
 * Resident Evil 5
 * Sonic the Hedgehog 2 and onward
 * The Subspace Emissary in Super Smash Bros Brawl
 * Tales (series)
 * World of Mana series

Assistant
Secondary characters help with some other indirect force as a part of the user interface.

Examples:
 * Jet Force Gemini lets a second player take control of Floyd after he's put back together. All the second player can do as Floyd is shoot enemies with what is basically an infinite-ammo pistol, except for specific areas where Floyd has to go it alone, where either player can control him.
 * Sin and Punishment: Star Successor allows a second person to control another gun. The second player doesn't have any charge shots or melee attacks, and doesn't take damage.
 * The Legend of Zelda the Wind Waker
 * Mechwarrior 3050 features possibly the strangest example, allowing a second player to take on half of the controls used in single-player mode to act as a “weapons officer.”
 * Super Mario Galaxy
 * The sequel expands on this by adding an orange Luma that can further assist Mario on top of the actions the second player did in the first game.
 * F-15 Strike Eagle is a Jet Fighter game for the NES that practically NEEDED an assistant on the higher difficulties. On 'easy', the jet would practically fly itself (auto-speed, auto-level, auto-landing), you had 1 type of multi-purpose missile, and 1 type of counter-measure. On the hardest difficulty there were 3 types of missiles, 2 types of counter-measures, and you had to handle all normal flight controls (speed/leveling/etc...). Needless to say, with only 4 buttons there were LOTS of multi-button controls to switch which missile was loaded, or which C-M to launch, or how to adjust speed. The second player's controller did nothing BUT these secondary tasks.

Progress in Turns
Essentially a single-player game where the game forces multiple players to take turns, a little like a Succession Game. Player 1 plays until he dies, then Player 2 plays until he dies, then back to Player 1, etc. Both players work toward a common goal and share progress. Individual players' scores may be tracked for competition.

Examples:
 * Super Mario Bros..
 * Donkey Kong Country