Falcon Kick (ファルコンキック) is Captain Falcon's down special move. Falcon bursts forward in a rush of fire a good distance forward, with reasonable start-up lag and wind-down lag. It has reasonable knockback and damage, and often hits characters in shorthops, but is difficult to pull off and avoid punishment.
Its use and physics has changed over the series, but in all versions, if the Falcon Kick goes into a wall (including the blocks in the stage Green Greens), he will bounce off and gain height, though this animation has a significant amount of ending lag.
In SSB, Falcon rushes forward, blazing with a flaming kick forward, with arguably the biggest hitbox out of all of its appearances in front of Falcon, and the most KO power. It travels enough distance to go from the lowest brown platform on Hyrule Castle to the top of the green wall in the "Tent" area. It has good range, and can KO at very high percents, where it launches foes at a 45° angle above Falcon. This move comes out fast as well, and is great to approach or punish. Falcon Kick, as with Falcon Punch, has its fire effects rendered as 2-D sprites. When Falcon hits a wall while using it, he bounces off and gains height, but this event is very laggy. There is a glitch where the move will "bounce" when used close to any ledge while facing the opposite direction of it. The only way to achieve this position is by rolling towards a solid platform's ledge, which appears to register a character as both on and (exceptionally slightly) off of said platform. This explains why the wall collision animation plays instead of normal aerial or grounded travel, as well as why certain other attacks (Kirby's Inhale, for instance) push the user off the ledge after jumping (with no horizontal controller input) from that spot.
There have been some changes to the move in Super Smash Bros. Melee, notably how he will regain his second jump after using this move in the air. The move lost a little speed and some KO power, but seems to travel farther and has better rendered effects (though a few red fire sprites appear in the move). This move is also easier to use near a ledge. The range is about half of Final Destination.
Despite these new factors, it isn't used particularly often outside of recovering due to his new throwing and aerial meta-game.
Due to the changed pacing of Brawl, the move is considered its slowest here, and has reduced stun. This move can travel about half the distance of Final Destination. However, due to the slower pace, it also makes a good move to punish foes, chase them while dodge rolling, or tech chase. Unlike Melee, it doesn't regain his second jump if used in midair.
The attack's sex kick properties make it unsafe on hit at lower percents. When it first comes out it has moderate knockback, though this initial hitbox is still not powerful enough to reliably KO under 150%. However, like Wizard's Foot its ending lag can be canceled if it is used in a position so the move ends in the edge very close to the stage, (nicknamed "Falcon Kick Canceling"), but unlike Wizard's Foot, hitting the opponent with the move slows Falcon significantly, and is punishable on lower percents, especially if going through multiple foes or if shielded.
In Brawl, Ganondorf's Wizard's Foot while airborne was given two initial hitboxes, one that spikes and one that sends the foe powerfully upwards, however this is not the case with Captain Falcon. In the air, Falcon will quickly go downwards at an slight left or right angle (depends on which direction he is facing), and if the foe is hit within the initial frames, they receive moderately powerful horizontal knockback. It has high duration, with similar frames to its grounded version, which however can also spell doom for Falcon players should they do the move off a ledge, as even with Falcon Dive's very large ledge sweetspot, Captain Falcon's falling speed may take him too far down. It can also be used when jumping off a grabbed ledge on the foe as a surprise aerial attack (though note the high ending lag when it hits the ground). Also just like Ganondorf's, Falcon can jump and immediately cancel it into this attack.
 Description from the Melee instruction booklet
Perform a sliding kick on the ground or a diving kick from the air.
 See also