Super Mario Bros. 3 contains a bizarre "vengeful Thwomp" glitch. Normally, if a Thwomp is hit by a hammer, it just dies. However, if a diagonal Thwomp is hit in the topmost position, it will perform a jump after dying just to get one last revenge attack in.
Using a combination of glitches in Super Mario World, Yoshi can be taken into the final battle, where he can eat Peach upon Bowser's defeat. With Peach gone, the ending will not play, and Mario and Yoshi will simply stare at each other forever.
The jump in storage capacity from Nintendo 64 cartridges to GameCube discs allowed the developers to be astonishingly generous with the storage in comparison. A Super Mario Sunshine cutscene of a single image fading in and out is larger than the entirety of Super Mario 64.