Undodog (also formatted as Undo Dog) is a helpful character first appearing in Mario Paint, selectable as an icon in the bottom toolbox in the Art and Music modes. He is a tan dog that has pointed ears and a square box around his neck like a collar, meant to represent his selectable square icon on a game menu. The box surrounding his neck was black in the original Mario Paint, but became white starting with Super Mario Maker. His name is a pun on the word "underdog", and a portmanteau of the words "undo" and "dog", and, as his name states, he helps the player undo the last action performed.
Undodog debuts in Mario Paint. His appearance in this game is that of a tan dog with a big head and a thin black box around his neck, like a collar, probably representing the outline of his icon. He will also dance and jump around at the bottom of the screen when the player is idle in the stamp editor or drawing board color selection. He will quickly run back to his original location if the player moves the mouse. If the player turns the game's music off and leaves it silent, Undodog will sometimes sneeze loudly. According to the instruction manual for the game, this is because of his allergies. 
Super Mario series
Super Mario Maker / Super Mario Maker for Nintendo 3DS
Undodog reappears in Super Mario Maker and Super Mario Maker for Nintendo 3DS with the same function as his original appearance: reverting the player's last edit whenever his icon is tapped. In this appearance, he has slightly more realistic proportions and he wears a white box resembling an Elizabethan collar instead of a black box. He also appears throughout the game outside of the course editor such as in the game's manual with Mary O. and Yamamura, riding a Reset Rocket in the background in Course World and when a player completes the 10-Mario or 100-Mario Challenges, and in the corner during Gnat Attack. When 10 seconds remain on the timer in Gnat Attack, he will start barking and jumping excitedly. If the player shakes the heart SFX, its icon will turn into Undodog wearing a surgical face mask. This SFX will cause static to appear briefly with a buzzing sound followed by the course's music turned off temporarily (or permanently, if it is equipped to Mario). The icon and the music being turned off is a throwback to Mario Paint where the bottom lever in the background music option has a similar appearance and effect when selected. A special event course titled "Walkin' with Undodog" also exists; completing it for the first time unlocks the Undodog costume.
Super Mario Maker 2
Undodog reappears in Super Mario Maker 2 filling similar roles and having the same appearance as in Super Mario Maker. However, he also has a larger role in the game's story mode (appearing for the first time as a 3D model), providing Mario access to various jobs to help rebuild Peach's Castle. At the beginning of the story mode, Undodog excitedly jumps around and mistakenly presses the Reset Rocket button on the ground, completely erasing Peach's Castle. At the end, after the castle is entirely rebuilt, Undodog goes over to the Reset Rocket again and looks at it happily while everyone gasps off-screen. In the postgame, the castle is still standing, implying that Undodog left the button alone. Undodog can also be seen in the background of nighttime levels in most themes riding the Reset Rocket.
Undodog talks to Mario as if he is a pet and even refers to Mario as a "good boy", while on the other hand Mario talks to Undodog by saying phrases such as "woof" and "bark". Additionally, after completing Story Mode, Undodog will tell the player jokes for 100 coins each. Ten jokes in total are told, with most referencing several in-game Course Maker elements, highlighted in blue in the jokes. Once Undodog runs out of jokes, the player can hear a previous one again for free, chosen at random.
Super Mario Maker for Nintendo 3DS
Super Mario Maker 2
Names in other languages