Koopa Klaw
Koopa Klaw is the Forward B move of Bowser in his Super Smash Bros. Melee appearance. It is a powerful claw swipe to enemies farther away, but also causes Bowser to grab onto enemies very close to him. It has the unique ability of allowing Bowser to grab onto an opponent in midair. Also, if an opponent that is close by gets hit, not only will they sustain damage from the swipe, but get bitten by Bowser's insanely sharp teeth, ouch!
Flying Slam
In Super Smash Bros. Brawl, the move has been reworked as Flying Slam. Bowser can now grab further and if he grabs an enemy, he'll flip in the air with the enemy and body slam them. Bowser's air movement can be controlled greatly during this move.
This special attack is shared by Giga Bowser, both in his boss appearance in Super Smash Bros. Melee and perhaps in his playable appearance in Brawl.