For the condition that occurs causing characters to shake back and forth while immobile, see Paralyze.
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

When characters are stunned, they are dazed for a few seconds and cannot perform any actions. The only ways for a character to recover is by flinching, waiting out the condition, or by button mashing to reduce duration.

Unlike most other status effects, characters can escape being stunned easier at higher percentages (whereas asleep, 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.

The sound effect of being stunned is 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.

Causes of Stunning

By moves

Moves Condition Games
Reflector shattering Projectile damage increases with each reflection. If overloaded, it will break the character's reflector.    
Shield break If one's shield is overused, it will shatter. If pulled off correctly, Mr. Saturn, Marth's Shield Breaker and Donkey Kong's Headbutt will break opponents' shields and stun them.        

By characters

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

By items

Item Attack Games
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 a whole bunch of damage will occasionally result in the trapped character being stunned upon breaking out.

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.