So, since we lost the last thread, let's pick up again where we left off.
All fighters have access to custom moves, potential replacements for each of their B-moves. Most of them just sacrifice some power/range for new utility (or vice-versa), but a few of them have new abilities entirely. You can unlock special moves through single-player activities and Smash Run, but Palutena and the Mii Fighters have access to theirs right from the start.
Here's a list. Note that this obviously contains spoilers for all the playable characters on the roster.
Note that Custom Moves, like the Mii Fighters themselves, can only be used while playing in single-player, local multiplayer, or in "With Friends" online multiplayer. While the lack of Mii Fighters is understandable since random anons probably don't want to see the dick you drew on your own face, I'm not really sure why custom moves are cut from "With Anyone" multiplayer.