Helpless (also known as freefall, special fall and various other names, and called "fallspecial" in game data) is a state in which characters are unable to take any action, with the exception of grabbing a ledge, maneuvering left/right, fastfalling, or climbing a ladder, until they land on the ground or pass a blast line. Helplessness is typically associated with just having used one's triple jump, although it also occurs after using certain other special moves (usually ones which help recovery). Many special moves involving controllable projectiles (such as Ness's PK Flash and Zelda's Din's Fire) cause helplessness as well in all games besides Ultimate.
Helplessness most commonly ends upon landing on the ground or being KO'd, although it also ends if characters flinch, allowing them to attack or re-use their triple jump. A helpless character is denoted by both a flickering black overlay and a distinct falling animation.
Curiously, the helpless state gives characters an extra ability in Super Smash Bros.: the ability to fall through soft platforms without landing on them. Starting in Melee, this can be done at any time (not just when a character is helpless).
Moves that invoke helplessness
Landfallspecial and "superdashtechnique"
As a unique animation is used for falling while helpless, characters enter a different animation than usual once they land on the ground. This is called "landfallspecial" internally in Melee. Because air dodging enters this state and wavelanding involves air dodging into the ground, when wavedashing is performed, Melee's debug menu shows "landfallspecial" as the character state. This originally led some players to believe that the "landfallspecial" designation was specifically designed for wavedashing and that developers intentionally put wavedashing in the game, further fueling the various debates over wavedashing's legitimacy. At one point, the myth morphed to where, instead of just "landfallspecial", there was purportedly another debug mode designation — cited as "superdashtechnique", "superdashattack", or other supposed variants — created solely for the wavedashing animation. All incarnations of this story have been proven false, and should not be themselves taken as evidence that wavedashing was intentionally put or left in Melee.
Freefall Carryover Drift
In Ultimate, if a fighter uses a special move which will put them into freefall, but they land before entering freefall, they may enter a glitched state if the special move's ending lag doesn't transfer from an airborne to a grounded state. Upon entering this state, the next time the character enters the air, they will initially adopt their normal air speed, but after a few frames will revert to the air speed they would have when entering freefall from the special move used, which is usually lower than their normal fall speed. This will persist until they double jump, grab a ledge or land on the ground again.