From Sonic Retro
In Chaotix, the Wall Jump can be used to scale walls as Mighty. Simply aim back towards the wall, and continually jump off of the same wall. When a character capable of using the Wall Jump jumps again while pressed against a wall, they will kick off of the wall, propelled diagonally upwards.
Mighty has the move as an intrinsic skill in Chaotix. In Unleashed (360/PS3), Sonic must find the Wall Jump Shoes in Spagonia's Entrance Stage before he can use it, while in Unleashed (PS2/Wii), Sonic Colours and Sonic Generations he can perform the move immediately. In Sonic Lost World, wall jumping is part of Sonic's Parkour moveset. In the Super Smash Bros. series, Sonic is one of select characters who are capable of performing the move in all of his appearances.
The Avatar in Sonic Forces is also capable of performing the Wall Jump, but they can only use this action in Imperial Tower. Through modding, it is revealed that Modern Sonic also has the move, but there is not a single instance in any of his stages where he can use it.