What are some cool abilities/skills/magic that lets you explore the world better?

I'm thinking of both magical and non-magical abilities.

Things like:

• Lockpicking (could be magical or just physical)
• Bashing through / blowing up a door
• Lifting up / breaking a boulder
• Double jumping / High-jumping
• Climbing walls/cliffs
• Breathing underwater
• Freezing a bridge over water
• Walking across water
• Making a bridge of wind over a chasm
• Rope arrows (a'la Thief)
• Walking through fire
• Melting ice
• Hacking into a computer console to open a door

What are some of your favorites? Got any good ideas for exploration-unlocking abilities you've never seen used before?

• Flight.
• Teleportation.
• Traveling through power lines or some other sort of conductive media.
• Astral / dream travel.

I rather enjoyed Wonder Boy 3 which opened up new areas to explore when you shape shifted to different creatures each having their own special abilities and weaknesses.

Astral / dream travel.

Freeze gun (freeze enemies so you can safely walk on them)

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.

I know this is not 'cool' to most but: simply getting more powerful. Is great fighting prowess a 'cool ability'? To some people it is.

Gothic 2 NotR did it and I loved the feeling of gaining more and more strength and increasingly powerful swords (armor too, although that is very rare in Gothic games and tied tightly to the plot) which allowed me to explore increasingly more and more dangerous areas to get even more power (often loot, sometimes weapons and scrolls, always some experience).

I guess it plays into my "mad with power" and "hoarder" personality traits. It also made it easier to apply willing suspension of disbelief on the game.

This kind of restricting movement in a world that is technically open is called 'Beef Gate': http://tvtropes.org/pmwiki/pmwiki.php/Main/BeefGate

They have an entry for Gothic, BTW and say it's 'practically made out of this trope'.

Repairing scenery and props

That was fun in some of the Paper Mario games.

Bullet time
Fast forward

In what way can these open up new areas to explore?

I'm trying to think of ways other than "Do you have X ability? Cool, door unlocked!"
I guess one method would be hitting a switch and having to quickly run to a timed door before it shuts. If the timing is intentionally too fast, you could slow down time to get inside (or have a coop player with you instead of time-slowing. ).

Or a crumbling bridge that collapses too fast for you to get across - if you slow down time, you could run across it before it crumbles.
This could even be done intentionally: Blowing up a pillar, and when it's halfway fallen down, run up it like a ramp and jump to the top of a wall before the pillar full falls to the ground.

These assume you can still move at the normal speed even when the world around you is slowed.
I can't think of any gating method where time-slowing or time-speeding would enable access to any area that you couldn't already reach if you happened to be really really skilled (which is cool game design anyway - accomplishing a difficult challenge without the easy solution).

I know this is not 'cool' to most but: simply getting more powerful. Is great fighting prowess a 'cool ability'?

One of two arm augs choices does that, yes. And leg speed aug lets you jump into crazy places.

Although by power and strength I meant actual combat prowess, but that DX does kinda well too with augs, skills and weapon mods if you're into combat over stealth.