Drop-In Drop-Out Multiplayer

In most video games, multiplayer is a matter of choosing the number of players at the start, and then getting a game going. This can be a problem if someone wants to join later. Ever have that situation where you're playing a game alone that you and your sibling both enjoy, then suddenly s/he walks into the room and wants to play?

The solution to that problem is Drop in Drop Out Multiplayer. The ability to join at any time, and just as crucial, the ability to leave at any time (which helps you avoid that annoying problem where your younger brother suddenly doesn't want to play anymore, leaving with a second character just standing there). These titles have no real distinction between single and multiple-player games, since those initiated as one type can easily turn into the other and back.

This solves more than just the sibling problem – it's also is what makes games with large player limits practical. The Game Lobby system, which requires players to get together ahead of time in a group and start the game all at once, would simply never allow for such games to happen by itself.

Since this means remaining playable with a fluctuating number of players, such games are usually either Co-Op Multiplayer or heavily reliant on bots.

General

 * Coin-op arcade machines (and many franchises originating from them like Gauntlet) will traditionally have “PLAYER 2 INSERT COIN” flashing perpetually over the upper right corner of the screen where P2's HUD goes, so that just dropping a bit of lucre into the corresponding slot will let any passerby join the game. This is especially useful with titles like the 6-player X-Men arcade game.
 * Ubiquitous in competitive online games, if for no other reason than to account for the possibility of some players experiencing connection problems in the early days. Now because, especially with Massively Multiplayer games having thousands of players in one level, and even many “normal” 100+ player games like Battlefield or Enemy Territory, it would be almost impossible to get everyone together for a session in unison (though clan and LAN players try valiantly.)
 * Games not particularly suited to this sometimes include aspects of it to deal with shortsighted players, especially games that tend toward lengthy matches. It's quite common, for instance, to see a larger Battle for Wesnoth game where half the factions have been handed over to remaining players, the computer, or spectators.

Other

 * Diablo is almost MMORPG-like, with players able to join and leave at will, form into parties, and the game even applying Dynamic Difficulty to compensate for the extra players.
 * Left 4 Dead has four characters at all times, regardless of number of players. Joining the game means controlling one of them, leaving means switching them back to AI control.
 * The Lego Adaptation Games do this. They typically have a second character following the first player around, and any player who joins instantly takes control of the second character. Quitting the game means that character becomes AI-controlled again.
 * Rock Band 3 introduced the ability for players to drop in/drop out at anytime, even during mid-song.
 * Playing as Sonic and Tails in Sonic the Hedgehog 2 or Sonic 3 and Knuckles, a player could grab the second game pad at any point to control Tails, while if there wasn't any input for about 30 seconds, the game will start controlling Tails again.
 * Similarly for playing as Helper in the SNES version of Kirby Super Star, except the game wouldn't take control of Helper until the second player's character died and was revived by the first.
 * Sword of the Stars even allows players dropping out to leave the AI some basic instructions on how to run their empire and password lock their slot, in case they intend to come back and retake command later.
 * Mario Party games allow you to set human players to computer players and vice versa at any time except during cutscenes and minigames.
 * In Mind Jack if you allow your game to be open other players can "hack" into your single player game, to help or to hinder.
 * Starting with New Super Mario Bros Wii, Nintendo's new retro games including Kirbys Epic Yarn and Donkey Kong Country Returns take the approach of allowing players to join or leave only inbetween levels, but at least it's better than having to set the number of players ahead of time and have it be fixed. In addition, Kirbys Return to Dream Land allows players to drop in and out during levels.
 * The Warriors allowed a 2nd player to control another Warrior character any time they jumped in and when they drop out, the character goes back to AI control.
 * World in Conflict is one of the few online RTS games that has this, made possible by the fact that it has no base building, so new players join at any time during a match without any gameplay disadvantage compared to players who've been there from the start. They do have the disadvantage of having less time to score points and the game also penalizes you for joining the already winning team if there are vacancies in the losing team (reducing the maximum amount of units you can field at once).
 * Civilization 4 had this, though it was a real pain coming into an AI civ where you didn't know where all your units were,a dn had to immediately fortify them all.
 * Team Fortress 2: allows players to come and go; some severs will even populate "empty" slots with AI bots so that even a handful of humans can still play a (somewhat) meaningful round.
 * Fortune Street has the "Out To Lunch" option, where a player can take a break from playing and a computer AI will take over until the player opts back in. Notably, earning points allows you to purchase personality traits and roles to assign to your Mii that also determine the AI's general strategy. This is an unusual form of drop-in, drop-out in which existing players can leave and return, as opposed to new players joining.
 * Gears of War didn't have this at all. 2 added it to campaign co-op (with a bot replacing Dom). 3 added it to campaign co-op (with bots replacing your other 3 party members) as well as versus multiplayer. It is also possible to join a Beast or Horde game mid-stream, but it requires joining a friend's game through the X-Box menu.