New Game Plus
A New Game Plus (or "New Game+") is an unlockable video game mode that allows the player to start a new game after they finish the game at least once, where certain aspects of the finished game, such as experience or items, affect the newly started game. New Game Plus is also known as "replay mode", "remorting", "challenge mode" or "hard mode", or "New Game Ex".
The term was coined by the 1995 role-playing video game Chrono Trigger, but examples can be found in earlier games, such as Super Mario Bros. (in which Princess Toadstool "present[s] you with a new quest" featuring stronger enemies) and the original Legend of Zelda. This play mode is most often found in role-playing games, where starting a New Game Plus will usually have the player characters start the new game with the statistics and/or equipment they ended the last game with. Key items that are related to the story are normally removed so they cannot ruin the game's progression, and are given back to the player at the time they are needed; likewise, characters that the player acquires throughout the story will also not appear until their scheduled place and time, but will get the enhanced stats from the previous playthrough.
Games with multiple endings, such as Chrono Trigger, often feature a New Game Plus mode which allows the player to access the alternate endings more easily. Many games include special features that are unlocked upon starting a New Game Plus. In Sigma Star Saga, a special item is needed to unlock two of the four available endings; this item is unavailable on the first playthrough, but can be found in a New Game Plus game. This feature can also be used as an unlock trigger for replaying the game at a higher difficulty, such as in the various Mega Man Battle Network games and X-Men Legends II: Rise of Apocalypse. In Astro Boy: Omega Factor, the New Game Plus is actually included in the game's story, as Astro must use the game's Stage Select (the ability to travel through time given to him by the Phoenix) to find out how to avert the Bad Ending that is mandatory the first time around.
Some New Game Plus variations feature twists on the original game's campaign. In games like Viewtiful Joe and Castlevania: Lament of Innocence, completion of the game unlocks a new character on each difficulty and the player has the option to either start a new game as a new character, or to use the original protagonist. Parasite Eve and Vagrant Story, among others, contain areas of the game that can only be accessed after completing the game. Additionally, completing some games such as Resident Evil 4, and the Metal Gear series can unlock items that can be accessed in subsequent playthroughs. The developers of BioShock made its New Game Plus mode available as downloadable content.
Although this mode is typically found in RPGs, other genres also use this feature. In the psychological horror game Eternal Darkness: Sanity's Requiem the player must have Pius Augustus choose a different dark god in each playthrough, only in defeating all three is the true ending revealed. The Ratchet and Clank series allows subsequent playthroughs at an increased difficulty and the ability to further upgrade weaponry. Also, upon completion of some Ratchet and Clank games, the choice to play the game in a first-person perspective is unlocked. In the survival horror titles Dead Space and Dead Space 2, the player is capable of unlocking various backstory logs, advanced outfits, and item rewards, as well as keeping all their items from their previous save. The upcoming Deus Ex: Human Revolution Director's Cut for Wii U will feature this mode.
In some games that implement achievement systems, players may be required to complete a New Game Plus game in order to obtain certain achievements. Examples of this include the "Calamity Kid" achievement in the game Bastion, and the "Twice Nightly" achievement in Batman: Arkham City.
Clear game 
A slight variation of this is the clear game (also known as a "post-game scenario"), a special mode that is played after finishing the regular game. In this mode, the player is given the ability to continue playing after the story mode is completed, allowing them to see the effect of defeating the antagonist on the game world and complete any remaining side-quests. Dragon Warrior II for the NES and EarthBound for the SNES are early examples of this. Other games return the player to the point just before the last boss, such as Mega Man Legends 2 and Dragon Quest VIII. Some games like Fallout 2 do not make mention of a clear game, but rather allow the player to continue playing after completion with no side effects. The clear game in Mass Effect 2 is notable in that characters that died during the final mission stay dead, effectively locking quests that involved these characters. In many games with this feature, new challenges and levels are opened to give the player an extra goal; each of the .hack games featured a bonus dungeon after completing the main mission objective of the games. One of the most notable gaming franchises to use a clear game feature is the Pokémon series.