Launch resistance

Ike's super armour from his Aether move. Notice how Ike didn't take any knockback from the Critical Hit Final Smash, which often kills characters in one hit.

Launch resistance, also called knockback resistance or super armor, is a phenomenon that manifests itself during certain moves in all three Super Smash Bros. games. It is defined as a character not flying when hit during a certain time, or in some cases not flinching as far. Note that knockback resistance, as the name implies, only affects knockback. The attack's full damage will still be taken. Yoshi's Double jump, Snake's Cypher, Diddy Kong's Rocketbarrel Boost (On the ground) and Kirby's Stone are the only common moves with finite amounts of knockback resistance, while all other knockback resistance moves have infinite knockback resistance (extremely strong attack on Kirby's stone makes full knockback but no damage).

In Super Smash Bros.

Knockback resistance was limited to Yoshi's double jump cancel counter, Most characters while throwing, Giant DK at low percentages, and Metal Mario. Master Hand basically has infinite knockback resistance.

In Super Smash Bros. Melee

Yoshi retained his resistance, while Metal and Giant characters had their resistance decreased a whole lot. Giga Bowser also has some amount of knockback resistance when fought in Adventure Mode. Master Hand and Crazy Hand both have infinite knockback resistance. Captain Falcon also has very few frames of Launch resistance while using a Falcon Punch

In Super Smash Bros. Brawl

Many characters have knockback resistance, usually in the form of moves that give a temporarily infinite amount (a.k.a. super armor.) All of the moves are "super armor" unless otherwise stated.

Character	Moves	Conditions and Notes
Bowser	Giga Bowser	For the entire period of being Giga Bowser.
Diddy Kong's	Rocketbarrel Boost	Only the grounded version (not standard launch resistance).
Donkey Kong	Giant Punch, Spinning Kong and Carry Throw	Giant Punch: only if fully charged; while moving his arm forward but the attack needs to make contact with his left arm and before it is released. Spinning Kong: only the grounded version; just before he starts to release it (frames 10-16 first hitting on frame 19);if he leaves the ground with Super Armor frames when using the grounded version, a glitch will make the Super Armour frames last for the entire move. Carry: for the entire first second of the carry only.
Ganondorf	Flame Choke	In the grounded version, when holding the opponent off the ground; opponent also gets super armor. In the aerial version, the opponent gets super armour but Ganondorf does not, allowing for strange kills in places like Norfair or Brinstar
Ike	Aether and Eruption	Aether: After throwing his sword in the air, but before he leaps up towards his sword. Eruption: some frames after the special move button is released but before the sword hits the ground.
King Dedede	Super Dedede Jump	From the start until just before the apex of the jump.
Kirby	Stone	The entire duration, does not take any damage or knockback except attacks that do at least 25% on him do full knockback but no damage (eg. Critical Hit, King Dedede's fully charged side smash) (not standard launch resistance).
Olimar	Pikmin Order	During the first few frames
Pit	Mirror Shield	Grounded version only; while pulling the shield out: frames 4-6.
Pokémon Trainer	Fly, Rock Smash and Squirtle's Forward Smash.	Fly:The beginning of the ascension fimes: Frames 4-13, making it when jumping out of shield and also making it a very good combo breaker. Rock smash:When it gets the rock first frames. Squirtle's forward smash:While moving forward. Ivysaur has no super armour moves.
Snake	Cypher	Snake cannot be flinched by any hitbox that deals exactly 7% or less, regardless of the knockback of the individual hitboxes. Most multi-hit moves deal less than 7% per hit, so they usually cannot interrupt the Cypher (though they of course still deal damage) (not standard lauch resistance). (See this post and this followup post on SmashBoards for more details.)
Wario	Forward Smash and Wario Waft	Forward Smash: While moving forward: frames 8-12 Wario Waft: When fully charged, during the first few frames
Yoshi	Double-Jump	Yoshi gains (approximately) 3860mph-worth of knockback resistance, as measured by the post-Brawl stats (under the "top launch speed", though the unit "mph" is nonsensical). This means that Yoshi will ignore any knockback that would launch him at less than ~3860mph(approximately 150%). As he is damaged, of course, he takes more knockback from an attack with the same launching power, meaning that weaker attacks will begin interrupting his double jump when Yoshi is at higher percentages. None of this prevents Yoshi from being affected by hitstun (not standard launch resistance). (See this post on SmashBoards for more details.)
All Characters	All grabs except Olimar's grab including special moves that penetrate another character's shield such as Chomp, Egg Lay, Inhale, Super Inhale, Falcon Dive, Dark Dive, Flame Choke, Force Palm, Flying Slam (first frame only) (not standard launch resistance).	But in fact grabs do not have real super armor just when the first frame that a grab hits a victim they successfully connect and like grabs have higher priority the grab cancel the attack and thus the victim doesn't recieve knockback.

External references

A better 'Super Armor List' Thread: lists characters and their moves that have Super Armor, along with some frame data.

The Armor Project: explains how knockback-resisting moves that are not super armor work, including Snake's Cypher and Yoshi's double jump.