Some more interesting abilities from various games
Ori and the Blind Forest:
There's an ability called Bash that can be used on most enemies or projectiles - when used, it propels Ori in the chosen direction while sending the enemy/projectile in the opposite direction, allowing it to be used simultaneously as a movement ability, a weapon (enemies can be harmed by their own projectiles), and a puzzle-solving tool.
The Smash ability propels Ori downward at high speed (greater that falling terminal velocity) and breaks certain walls/floors.
Strider (2014):
Down Strike functions like Ori's Smash.
The player character can freely climb walls AND ceilings.
Plasma Catapult is a short-range dash/teleport hybrid which can be upgraded with elemental properties. The ice version freezes enemies when you dash through them, for an interesting take on the Metroid-style ice beam climb pattern.
The Down Strike can be cancelled into the Plasma Catapult for additional movement options - in fact, there are optional items that require skillful use of this trick in combination with the double jump ability to obtain.
Axiom Verge:
The game has an upgradable short-range teleport move - initially it only teleports the player through 1-tile-thick walls and is slow to activate, but as it is upgraded it gains fast activation, longer range, limited invincibility, and the ability to damage enemies and destructible objects in it's path.
The Address Disprutor, also known as the "glitch gun", allows the player to "glitch out" certain places to clear obstacles and reveal new platforms. It can also be used to "glitch out" enemies in a wide variety of ways - for example, certain enemies will break through obstacles you otherwise can't break yet when you glitch them.
The passcode tool allows the player to enter passwords which can have various effects on the game, including revealing new pathways. (Those specific passwords can be found in-game through various obscure means.)
The player gains the ability deploy a walking drone, which is your means of accessing areas too small for the player character to enter. Later the player gains the ability to instantly teleport to their drone's location regardless of distance.