A recovery is the attempt to return onstage after being knocked or falling off. Some tools to achieve this end are the midair jump and the "third jump" (usually an up special move). Some recovery moves only go nearly straight up, while others are for long horizontal differences.
For many characters, recovery can be augmented or replaced by moves other than the standard second jump plus up special. This page documents the maximum recovery potential of each character. In the case that a character has multiple recovery options for horizontal or vertical movement, both are listed.
List of recoveries
It is notable that in Super Smash Bros. Melee, an air dodge while tilting the control stick would allow some vertical and/or horizontal recovery, though it puts users in a helpless state. Note that if the recovery is the same in each game, it will not be mentioned. Due to increased floatiness and the fact that it's easier to grab a ledge, recoveries as a whole appear to be greater in Brawl and SSB4 than those in Melee and Smash 64.