For the condition that occurs causing characters to shake back and forth while immobile, see Paralyze.
For the effect when a shield is hit, see Shieldstun.
The result of Marth breaking Mega Man's shield in SSB4.
Mega Man stunned in Super Smash Bros. 4.

Being stunned or dazed (referred to as FuraFura in Super Smash Bros. Melee's debug menu and in-game files for Brawl, after the Japanese onomatopoeia for dizziness), an effect known as dizziness in Brawl, is a special condition that leaves a character immobile for a short period of time.

Summary

A stunned character is dazed for a few seconds and cannot perform any actions. They can only naturally recover by waiting for the condition to end. Button mashing and shaking the control stick reduces the duration of the effect, and suffering any amount of knockback ends it prematurely. Since Brawl, characters were given a short animation showing them regaining consciousness.

Unlike most other status effects, characters are stunned longer at lower percentages (whereas sleeping, for example, lasts longer at higher percentages). In Smash 64, the base time in frames that a character is stunned can be determined by the formula (400-damage)+60.

Stun is accompanied by a cartoony tweet sound effect that loops until the condition is stopped. This sound effect debuted in Melee, and its volume was increased in Brawl. In all games, characters also have a flashing red overlay applied to their model; in Smash 4, however, this only happens when a character's shield is broken.

It is impossible to be stunned while airborne.

Causes of Stunning

By moves

Moves Condition Games
Reflector shattering Attempting to reflect a projectile that deals above a certain amount of damage will shatter the reflector and stun its user.   
Shield break If a shield's HP drops to 0 or below, it will break and the user will be stunned.      

By characters

Character Move(s) Games
Luigi Negative Zone (Grounds aerial opponents and stuns them.)  
Mewtwo Disable    
Wario Garlic Breath (Custom move)  
A barely charged Wario Waft as Wario-Man   

By items

Item Attack Games
Assist Trophies Rathalos: Roars  
Deku Nut Any attack on the ground   
Poké Ball Pokémon Weavile: False Swipe  

By enemies and bosses

Enemy/Boss Attack(s) Games
Master Hand Snapper  
ReDead Scream  

By stage

In Wrecking Crew, getting trapped in a barrel and taking heavy damage will occasionally result in the trapped character being stunned upon breaking out. This can only be done with low-knockback attacks, however.

Gallery

Trivia

  • Bowser is the only character in Brawl to lack the tweeting sound effect while he is stunned. The reason for this unique property is unknown.
  • When Samus is stunned, her Power Suit starts to short-circuit, causing erratic and almost glitch-like movement.