Glitch

"Glitch" is the term applied to something strange happening in a Mario game, as well as any other video game. They are caused by programming errors within the game's coding. Arguably, the most famous (or infamous) glitch in video gaming history is the Minus World glitch from Super Mario Bros.

When glitches happen, either something unusual will happen (such as Mario being able to walk underwater, a glitch in Super Mario Sunshine and Super Mario 64 DS) or the screen will freeze and sometimes some random pixels and object tiles will appear. Some glitches are caused by damaged games. Some only activate when the player presses a certain sequence of button commands. Also, as seen in Super Mario 64, if a player is to tilt the game cartridge itself, Mario's limbs will be dislocated and he will sink into the ground. Other glitches, such as the aforementioned Minus World, can actually create new levels occasionally made randomly and haphazardly, and others allow players to guide their character off-screen. Sometimes glitches grant access to slapdash areas (sometimes composed of many garbled symbols) and unused parts of stages.

The full list of glitches can be found here.

Trivia

 * Glitches have been parodied and even used in the plot of Mario games. Examples of this include TEC-XX, who had the "glitch" of falling in love with Princess Peach in Paper Mario: The Thousand-Year Door, and Fracktail of Super Paper Mario, who shouts many lines of dialogue spoofing glitches and errors.