Characters that can Wall Jump (listed in alphabetical order to make it easier to find which characters can wall jump; NOT ranking them by numbers)

1) Captain Falcon
2) Falco
3) Fox
4) Mario
---Peach****
5) Pichu
6) Samus
7) Sheik
8) Young Link

***Note 1 - as you wall jump continuously (without landing of course), you lose altitude/height with each jump after jump. After about 30 or so jumps(on average about), you start to LOSE altitude and instead of going up you begin to slowly go down.

****Note 2 - Peach with her Forward B move(Peach Bomber) can "wall jump" over and over again without ever falling or losing altitude, as long as you press forward B over and over again FAST and CONSTANTLY. You can actually move UP with this, but it's a VERY slow and long process, though it's a great trick to stall matches on courses like Fourside, as many characters can't get to you and you can use this to cheaply win timed matches that you're winning. Your opponent probably won't like it much though.