Super Dedede Jump
Super Dedede Jump (スーパーデデデジャンプ Sūpādededejanpu) is King Dedede's Up Special Move. He jumps extremely high, then crashes down. If a foe is struck by Dedede's underside on the way down, they are spiked. If caught under Dedede's weight upon impact, they are shot at a 45-degree angle sideways. Foes can also be hit by two stars that appear at Dedede's sides upon impact with the ground. You can angle the jump by pressing left or right while Dedede is turning to face the screen before he actually jumps, but once in the air, you lose control over it. He is vulnerable when he lands, so one can cancel the move by pressing down if it looks risky. However, if it is done too close to when Dedede lands, he will become even more vulnerable, instead of just getting up, he will fumble around before getting up, forcing strategy when using the move. If Dedede hits a ceiling while using the move, he will fall helplessly.
Unlike most other up special recoveries in the game, this move does not auto-sweetspot the edge. However, if the move is canceled close enough to the edge, Dedede will snap to it. It is also possible to use the Super Dedede Jump as an edgeguarding move.
During the first half of this attack (when he jumps into the air) King Dedede can take damage, but cannot flinch. If he hits an opponent as he is falling, it becomes a powerful meteor smash. If this move spikes an opponent onto the ground, and then Dedede lands on top of them, it has vertical knockback instead of the normal 45-degree angle.
Stars are produced around King Dedede when he lands, similar to Yoshi's Yoshi Bomb, but are produced in reference to the Kirby games.
Amusingly enough, if this move is used under a Low-Gravity effect (through certain stages, such as Pirate Ship and Spear Pillar, or through Special Brawl options) Dedede comes down at ridiculously slow speed and can travel absurd distances horizontally. By the same token, its utility as a recovery move is hampered by high-gravity effects, but it becomes much more difficult to avoid.
The sound which is made while jumping is nearly similar to the sound made by zooming the map in The Legend of Zelda: The Wind Waker.
This attack can be used to avoid Lyn's sword strike if timed correctly.
If attacked while in the middle of the first half by an object that will normally catch a player, such as a smart-bomb, he will be frozen and sometimes get knockback or other times finish the jump.
The Super Dedede Jump is one of King Dedede's main attacks from the Kirby series, including his debut in Kirby's Dream Land. In the Kirby games, when Dedede lands, two stars would appear on each side of him in which Kirby could swallow them and spit them back at King Dedede, though Kirby can't swallow the stars in Brawl. Being able to cancel the attack and land normally is a new addition added in Super Smash Bros. Brawl, and makes it reminiscent of the "High Jump" ability from Kirby's Adventure and its remake, Kirby: Nightmare in Dream Land.
 Description from the Instruction Booklet
Jump high and come down with massive force. You can cancel the move by tapping the Control Stick down.