I kind of always wanted to make a video like this.

Reddit post:   / video_which_character_jumps_the_furthest  

Possible improvements:
C.Falcon: 1) Use downB off the platform to gain 1 more meter.
2) Might gain more distance by "boost run" before jumping (says sNills)
Mario: Might be able to use sideB (says SNB_Boat)
Kirby: Can aerial to bypass a rejump height cap (says sugamton)
Jigglypuff: Same as Kirby.
Mewtwo: Can possibly extend his double jump by doing backaerial (says Cohenski & Nick Hooper). Also can possibly use sideB.
Pikachu: Can upB in the same direction twice by doing specific inputs (says typhyr)
Pichu: Same as Pikachu.
Fox: Might gain more distance by shining after the 1st jump (suggested My Miscellany)
Falco: Same as Fox?
Peach: 1) Might be able to use neutralB (said My Miscellany)
2) Use aerial right before the float ends (said My Miscellany)
Ice Climbers: Might gain more distance when they are two (said l5555l)
Samus:    • Samus Long Jump (TAS)  
Instead of upB, use airdodge and immediately tether.
Game & Watch: Might be able to use downB (says ssbmslurppp)