Ike's super armor from his Aether move. Notice how Ike didn't take any knockback from the Critical Hit Final Smash.

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 as far when hit during a certain time, or in some cases not even flinching. Note that knockback resistance, as the name implies, only affects knockback. The attack's full damage will still be taken. Yoshi's double jump and Snake's Cypher are the two common moves with finite amounts of knockback resistance, while almost all other knockback resistance moves have infinite knockback resistance.

Yoshi: during his 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. 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 hitlag. (See this post on SmashBoards for more details.)

Snake: during his 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). (See this post and this followup post on SmashBoards for more details.)

In Super Smash Bros.

Knockback resistance was limited to Yoshi's double jump cancel counter, Most character's 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.

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):

Character Moves Conditions and Notes
Ike Aether and Eruption Aether: before he leaps up towards his sword.
Eruption: after the special move button is released but before the sword hits the ground.
Bowser Giga Bowser, Flying Slam, and Bowser Bomb For the entire period of being Giga Bowser, and while he is in the air (first frames) for Bowser Bomb. Flying Slam is explained below.
Snake Cypher Not actually Super Armor, but Snake will not flinch from any hit that deals exactly 7% damage or less.
Donkey Kong Giant Punch, Spinning Kong and Carry Throw Giant Punch: only if fully charged; while he is in yellow color and after that attack his hand before it is released.
Spinning Kong: only the grounded version; just before he starts to release it.
Carry: for the entire first second of the carry only.
Ganondorf Flame Choke Only the grounded version, when holding the opponent off the ground; opponent also gets super armor.
Pokémon Trainer (Squirtle, Charizard, Ivysaur) Fly and Squirtle's Forward Smash. Ivysaur has no super armor moves.
King Dedede Super Dedede Jump From the start until just before the apex of the jump.
Pit Mirror Shield Only while pulling the shield out.
Olimar Pikmin Order During the beginning.
Wario Forward Smash: While moving forward. Wario Waft: When half charged or fully charged, just after the release of the attack.
Yoshi Double-Jump Not actually Super Armor (as described above), but lasts through the entire jump.
All Characters All grabs (first frame only) The very first frame that a grab hits a victim, including special move that penetrate another character's shield such as Chomp, Egg Lay, Inhale, Super Inhale, Falcon Dive, Dark Dive, Flame Choke, Force Palm, Flying Slam.

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.