Thunder (Pokémon)
Thunder is Pikachu and Pichu's Down Special Move.
In Super Smash Bros. and Super Smash Bros. Brawl, only Pikachu has this move. In Super Smash Bros. Melee, both Pikachu and Pichu have it.
In Super Smash Bros., this move has infinite vertical range and thus can be used to score KO's when an opponent is near the upper Blast line. This is called thunderspiking, and can lead to much lower damage kills. As a result, Pikachu players try to integrate it into their combos as often as they can, typically after an up-smash. Though the move is powerful, it has considerable ending lag, especially in Melee.
In Super Smash Bros. Melee, Pikachu/Pichu call out and a cloud appears high above them, a lightning bolt then strikes down from it, hitting either the first platform or Pikachu/Pichu themselves. If Pikachu/Pichu are hit an extra explosion of electrical energy is created that can do extra damage. Pichu incurs 3% damage if the bolt strikes it, making it the only special Pichu has that might not damage it.
While it may seem that this move does not have a cloud, it does, but it is not very apparent unless on stages such as Hyrule Temple.
In Brawl and Melee, the thunder portion of the attack is considered a projectile and can be reflected back at Pikachu or absorbed for health. The explosion can not however. Also in Brawl, Thunder can pass through platforms that are close enough to the cloud. This is best seen in Hyrule Temple if Pikachu uses Thunder on the bottom portion of the stage. Also in Brawl and Melee, the off screen cloud portion of the thunder attack can be used as a KO hit if the player being hit is high enough in the air. Pikachu is helpless while initiating Thunder.
An interesting property of this is that if this attack connects with Pikachu in mid-air, Pikachu will bounce upwards a bit. Due to its startup time, it won't aid much in recovery, but is useful to Guard Break, especially against spikers. If used near the edge of a stage, the Thunder can create a wall of electricity to prevent a recovering opponent (especially if Thunder Jolts are sent out beforehand), best if they try to go for the ledge.
Pichu's Thunder deals more hits and has slightly more vertical knockback than Melee Pikachu's Thunder.
Origins
Thunder is based off a move of the same name in the Pokemon RPGs. Thunder is well known for its very high base power of 120 and for being the strongest electric type attack since the first Generation of the Pokemon games. It is also known for its low accuracy of 70, causing it to not be too reliable. However, if the weather effect is rain, its accuracy becomes perfect and even has a 30% chance to break through the move "Protect." Even without rain, the move is capable of hitting an opponent that is in the "flying" state (after using the move "Fly" or "Bounce" but before it strikes). Another advantage over the generally more reliable Thunderbolt is its 30% chance of paralysis. In competitive play, Thunderbolt is often chosen over Thunder for being generally more reliable (an accuracy of 100 vs. an accuracy of 70). In Uber battling however, Thunder is almost always chosen over Thunderbolt due to the prominence of Kyogre, who's ability Drizzle, causes an eternal rain effect. As such, the commonality of Kyogre causes Thunder to often have the perfect accuracy bonus in Uber battles.