Wall of pain
The wall of pain, often abbreviated to WoP, is a Jigglypuff technique which involves barraging the opponent with fast aerial attacks, exploiting Jigglypuff's high horizontal air speed to weave back and forth. The Wall of Pain can be used as either a method to juggle enemies offstage, as a powerful edgeguarding technique, or as a method to increase the damage on opponents. In all four games, the technique is among the most powerful in Jigglypuff's metagames, and proper use of it is important for use of Jigglypuff in tournaments.
Overview
On the ground, Jigglypuff should move forward in the air with each attack, then once the opponent is hit, move back to the place where the Wall of pain was started. This allows for quick attacks and keeps Jigglypuff out of range from any retaliations. In Super Smash Bros. Melee, this is done by interspacing Jigglypuff's back aerial with jumps while moving off the stage, utilizing Jigglypuff's superior air maneuverability to always land a hit with each spin kick.
In Brawl, the back aerial has lost its knockback, and the forward aerial has had its increased, which allows for an easier WoP, since Jigglypuff does not need to face backward. Therefore, when on the ground, or working up damage, the back aerial WoP is utilized to keep the forward aerial fresh, but for juggling off the stage at higher damage, the forward aerial, with greater knockback, works better. Stale-move negation means that switching between the two, if possible, has a greater effect. Pound can be incorporated into the WoP if used solely for working up damage.
In Smash 4 Jigglypuff's back aerial has much more knockback again and is designed as a finisher rather than a combo move, making it easier to finish a WoP with a back aerial but harder to keep one going. As such, most WoP's in Smash 4 generally utilize Jigglypuff's forward aerial (and neutral aerial as a finisher) instead.
Smashers Tetsuya and AOB were the earliest prominent users of the technique, and they are largely responsible for its widespread use. The term "wall of pain" was coined by SmashBoards administrator and retired smasher Amorasaki, a longtime friend of AOB.
Other characters
While other characters also have midair jumps, most do not have the appropriate recovery potential, air speed, or falling speed in order to fully emulate Jigglypuff's Wall of Pain. Wolf, Kirby, King Dedede, Meta Knight, and Bayonetta, however, can perform similar techniques. Some other characters, such as Captain Falcon in Melee, may have "pseudo-Wall of Pains" with similar outcomes, which however are not based on a back air.
Kirby
In Melee, Kirby can use a similar technique to the Wall of Pain with his back air. Called the Fence of Pain, due to having more "holes" than Jigglypuff's Wall of Pain, the technique is arguably Kirby's most powerful in his otherwise weak Melee metagame.
The technique returned in Brawl and, as a result of Kirby's improved air speed in the game, it is arguably as powerful as Jigglypuff's Wall of Pain.
Kirby is still capable of performing a wall of pain in Smash 4 using his forward aerial, sometimes being able to carry opponents entirely off-stage from 0 percent. This wall of pain requires proper reading of the opponent's trajectory to use, and typically won't work against fast-fallers or those with high air speed.
Meta Knight
In Brawl and SSB4, Meta Knight can potentially use his back or forward aerial attacks in order to perform a pseudo-Wall of Pain. The presence of the Sakurai angle in these attacks, however, prevents the attacks from consistently sending opponents in one expected direction, and Meta Knight's below average air speed hinders his ability to pursue opponents. His long, safe recovery, however, makes this Wall of Pain of rather low risk to perform.
King Dedede
In Brawl, King Dedede has his own wall of pain with his back air. It is arguably as useful as Jigglypuff's due to his back air's speed, lingering hitbox, short duration, and decent power. However, it can be difficult to continue chasing opponents with it due to his very fast falling speed and incredibly low air speed, though his low gravity as well as his long, hard-to-intercept recovery can reduce the risk of using this technique.
Wolf
In Brawl, Wolf can use a wall of pain with his back air, which is often considered a useful strategy for him due to his very high air speed and his back air's speed, power, and range. However, his very poor recovery and fast falling speed make it very risky to perform.
Bayonetta
In Smash 4, Bayonetta has a wall of pain in her forward air, which is a three-hit combo and raises her slightly in the air with each use.