Falcon Dive (ファルコンダイブ Farukon Daibu) is Captain Falcon's up special move. Contrary to the name, Falcon does a leap in the air, fist extended while glowing green. If Captain Falcon catches the foe while still ascending, he'll grab the foe and launch off with a cry of "Yes!". The attack cause an explosion and burns the opponent after Captain Falcon launches. If a hit is scored, the move can be used again; if not, Falcon becomes helpless. When used on the ground or in the air, it can be reversed.
Falcon Dive can easily stage spike opponents while allowing Falcon to recover.
In Super Smash Bros., this move was Falcon's main recovery move, other than the Falcon Punch angled upwards (which gave him a slight vertical and horizontal boost).
When the move connects with foes, it will strongly launch them at a 45° angle horizontally and vertically, thus making it hard to DI the knockback. It does a solid 20% damage upon connection with high knockback (average KO is around 130%). As with all of Falcon's special moves, it had 2-D rendered sprites as special effects. When contact is successful, it will restore a foe's midair jump and Falcon will be not be helpless, free to use the move again.
A string of multiple up aerial attacks from Captain Falcon followed by a Falcon Dive, throughout all of the games in the Smash Bros. trilogy is commonly referred to as an "SSB64 Combo", as this was a very common combo in said game.
Not much has changed since its Smash 64 incarnation aside from better voice quality and better special effects, along with the move travelling a much further distance upward, though the hitbox isn't out for as long. Falcon Dive seems somewhat weaker and easier to DI the angle. As with Smash 64, contact will allow the foe to reuse a midair jump and give Captain Falcon the ability to use the move once more.
In Brawl, Falcon Dive was buffed in terms of how easy it is to land, but the knockback was nerfed. Timing and landing the move seems to be improved due to the floatiness and the slower falling speed of characters in Brawl. However, doing it in the opposite direction Falcon is looking drastically decreases the horizontal distance which decreases the recovery distance and didn't happen in Melee. Also, Captain Falcon is vulnerable to hits during the start-up and to moves that hit directly above him (where the move has no grab box).
A number of things were changed from its Melee function to Brawl's. Raptor Boost's base knockback no longer allows Falcon to combo into it as effectively as before, and a majority of Falcon's remaining combos into the Dive are much more predictable and DI-able. It no longer restores a foe's midair jump, though Falcon can still use the move afterwards. This move cannot break Smash Balls but it is capable of destroying targets in Target Smash!! when the body comes in contact with the target.
Perhaps the biggest change and buff of the move from Melee to Brawl is the ability to grab and effectively stage spike foes that hang on the ledge much more efficiently; Falcon Dive will grab foes hanging onto the ledge and function as it normally would airborne, making Captain Falcon harder to edgehog than ever before, though it's still vulnerable to edge hogging if the edge hog is timed early enough, especially because his ledge sweetspot range is one of the largest in the game. It is excellent at punishing foes who camp on ledges. This is considered one of Captain Falcon's few buffs from Melee to Brawl.
 Description from the Melee instruction booklet
Grab an enemy then propel him or her into the air.