The move is unique to the Super Smash Bros. series, but Captain Falcon famously performed a Falcon Punch in the F-Zero animated series, F-Zero: GP Legend, where he uses it to defeat Black Shadow. (See this video.) It has become quite memetic, as the clip makes it appear that the Falcon Punch causes an explosion that can be seen from space. (In reality, the blast is from Black Shadow's self-destructing base, and Captain Falcon is merely using the Falcon Punch to prevent Black Shadow from escaping said explosion.) This is reinforced in a Subspace Emissary cutscene, when Captain Falcon performs a Falcon Punch on a giant R.O.B. in a very similar fashion to the clip from the animated series.
As a testament to the move's popularity, it seems to have come full circle and crossed back over into F-Zero canon: it is mentioned in F-Zero GX's ending song, specifically in the line "When a mighty illusion threatens your lunch / Falcon will be unleashing the Falcon Punch."
Here's what would happen if captain falcon's final smash wuz this http://m.youtube.com/index?desktop_uri=%2F&gl=CA#/watch?v=FFtw7qW7Vcw
1.Falcon would call in the blue falcon
2. Falcon would epic punch however many people he hit each person hit would get 100 damage from it and they would fly very far
3.the explosion from the aftermath would cover the entire stage causing at least 20 damage to whoever gets hit
I know ur thinking "but that's way to cheap man!" but it would probably move him up a tier. His moves actually are kinda bad.