The Air Not There

A consequence of the Rule of Perception: Air, which you can't see, doesn't actually exist.

Some applications:

If you stop time, so that everything in the world is frozen in place except you, you can move around easily; you are not held immobile by the air molecules frozen in place around you. (Suffocating is also not a problem.)
If you can travel at Super Speed, you don't have to worry about air resistance or friction.
If you are teleporting somewhere, it's important to arrive in an empty space where you won't be intersecting any solid objects, but you don't have to worry about intersecting the air molecules that are probably swarming through your empty space.

Frictionless Reentry: Atmospheric resistance and friction don't exist for spacecraft entering and leaving a planetary atmosphere.
Batman Can Breathe in Space: Since breathing on Earth is possible and air is not there, it should be just as easy to breathe in space when the air is also not there.

For characters with superpowers, may be a consequence of Required Secondary Powers.

Examples of The Air Not There include:

Played Straight

Film

Clockstoppers has hypertime watches that effectively stop time by making the wearer move really, really fast. The atmosphere never presents any problems.

Literature

Frank Herbert's Heretics of Dune
The Girl, the Gold Watch and Everything by John D. MacDonald
Momo, from the novel by Michael Ende, can move just fine even when everything else has been frozen in time.

Live-Action TV

Star Trek: The Original Series episode "Wink of an Eye"
The Wild Wild West episode "The Night of the Burning Diamond"
UFO episode "Timelash"
The Twilight Zone TOS episode "A Kind of Stop Watch"
The Outer Limits TOS episode "The Premonition"
Star Trek: The Next Generation episode "The Next Phase". Geordi and Ro are accidentally phased so that they can pass through solid matter, but breathing (which is inhaling tiny particles of unphased matter) is not an issue. Nor is walking on unphased floors.

Aversions

Anime and Manga

Generally averted in Kimagure Orange Road: when the Esper protagonists teleport, it always causes a short but violent air displacement, both at the spots of departure and arrival. One episode feature the variant of time-stopped people ignoring air, though.
In Dragonball Z, Guldo of the Ginyu Force can only stop time as long as he can hold his breath. This makes sense, since he wouldn't be able to breathe if the air was frozen in place.

Comic Books

Nightcrawler from the X-Men goes "BAMF" on teleporting in and out because he's displacing air molecules.
- The sound is actually the air collapsing on the space he has suddenly vacated (the 2nd movie actually uses a very realistic sound for the collapse of a human-sized vacuum). Why he also makes the sound when appearing, on the other hand . . .
The various speedsters know as The Flash all have an aura specifically to protect them from air friction. (Wally West even once removed it from someone he was carrying...)

Film

In The Incredibles, when Edna Mode explains to Helen about the suits she designed for the Parr family, she mentions specifically making Dash's suit out of a material that can "withstand enormous amounts of friction without heating up or wearing out" so he can run hundreds of miles per hour in it.

Literature

In the Discworld novel Thief of Time, the Monks of History use special equipment to slow down time relative to themselves, but can still move and breathe because the time dilation field extends beyond their own bodies.^{[please verify]} This would have unfortunate effects if the field partly eclipsed a living thing, so extreme care with the equipment is needed.
- Note that this trope is justified for Susan, who has no special equipment or training to shield herself from the time-stoppage, yet doesn't need to worry about obstructing air molecules because walking through objects is one of her occasional talents as Death's granddaughter.
In H. G. Wells's short story "The New Accelerator", moving thousands of times faster than normal causes the protagonists to heat up due to friction with the air.
In the Doctor Who Tie-in Novel Nuclear Time, when the Doctor's personal timeline briefly un-reverses, he chokes on air that is suddenly being inhaled rather than exhaled.
In Sergey Lukyanenko's The Stars Are Cold Toys, it is strictly forbidden to activate the jumper prior to exiting the atmosphere. The protagonists are forced to do this when escaping, even though they know the displaced air may cause hurricanes.
The Cyborg and the Sorcerers by Lawrence Watt-Evans is one of the few works with a Disintegrator Ray to consider the issue of the ray having to disintegrate all the intervening air molecules before it reaches its intended target.
Every instance of teleportation into air in the Young Wizards series is accompanied by a loud bang of displaced air, frequently described as sounding like a gunshot or a car backfiring. The gust of air has also knocked stuff over at least once.
In Good Omens, when the Hellhound transforms into a small terrier as per his master's wishes, the narration makes reference to the sound caused by air rushing into the vacuum it had previously occupied.

Live-Action TV

It is subtle, but when ships perform FTL jumps in the 2000s version of Battlestar Galactica, they cause a small, localised vaccuum around them. When air is present (inta-atmos jumps, leaking from space stations, etc.), it is seen getting sucked out alongside the jump. It should be noted that the FTL "bubble" around the ship sucks in any matter, not just air. This was shown on several occasions, first when Galactica jumped just above the surface of New Caprica, causing huge gusts of wind as more air filled the newly-created vacuum, then when Boomer's jump away from Galactica tore the ailing ship's hull and later when a group of Raptors jumping from the unused landing bay caused the whole bay to rip like paper.