A SMAAAASH!!, or a SMAAAASHing hit as described by a Friendly Mole, is the Mother series's equivalent of a critical hit; it is a random occurrence in which an attack deals about twice as much damage. This can only occur when using a character's normal attack, such as "Bash" or "Bite".
In EarthBound Beginnings, Smash Attacks are a rare and powerful move that occur at random and completely ignore the target's Defense. A well-known glitch in the Famicom version is that instead of the "SMAAAASH!!" being its normal color, it might accidentally use an enemy's color palette (i.e. a purple SMAAAASH!! against a Mr. Bat).
The chance both to deal and to prevent a SMAAAASH!! attack in EarthBound Beginnings is affected by the stat Fight.
When a character in the player's party deals such an attack, the screen flashes green twice and "SMAAAASH!!" appears in the text box on the upper side of the screen. If a character from the player's party receives a SMAAAASH!! attack, the screen will instead flash red once.
The chance of dealing a SMAAAASH!! attack in EarthBound is affected by the character's Guts. Surprisingly, the Luck stat has nothing to do with it. Jeff cannot SMAAAASH!! in the SNES and Super Famicom version, because he only uses Shoot weapons. However, in Mother 1+2, Jeff can hit a smash. This is probably an error.
In Mother 3
SMAAAASH!! attacks in Mother 3 work the same way that they do in EarthBound, except that "SMAAAASH!!" appears above the victim's sprite if dealt to an enemy, and above the character's HP meter if dealt to the player's party. Flint's "Power Smash" Skill is the only non-bashing attack that can SMAAAASH!! enemies; this skill always results in a SMAAAASH!! if it hits.