In Super Mario World, grabbing a Mechakoopa in Bowser’s Castle and turning around while holding it will seemingly make Mario disappear for a few frames. However, looking closely, we can see that Mario’s feet and torso are still present during the transition, so it is only Mario’s head that is disappearing.
By performing sequence breaking in Paper Mario: The Thousand-Year Door, it is possible to enter the Crystal Star room in the Great Tree in a glitchy state. Some of the effects include Mario’s sprites being layered improperly, walking in mid-air, and falling through the ground. (Source)
In Super Mario Bros. 2, taking a key from a Phanto room, exiting the room, and re-entering it will result in two Phantos chasing after the player until he leaves the room. (Footage recorded by me from a NES emulator.)
ifesbob 