Shockwave Clap

Clapping is pretty loud, but it pales in comparison to the Shockwave Clap. Sometimes it's just a really loud clap and sometimes it has the power to knock people over or cause physical damage. It can have more intuitive uses from time to time, such as blowing out fires.

This is commonly used by characters with Super Strength, since it lets them demonstrate their power without directly attacking someone (which could have messy results). Usually appears in the form of a powerful, high-pressure wave of air.

The "realistic" varieties of Sword Beam create a similar effect, but concentrated into a sharp edge. However, these are usually associated with skill rather than strength.

Examples of Shockwave Clap include:

Comic Books

A trademark move of both Fantastic Four's The Thing and the Hulk.
- In a notable instance, at the end of the Fall of the Hulks storyline, the Hulk uses this to stop a building from collapsing by using the shockwave to fill the building with sand (he was fighting on the beach).
Luke Cage, Hero for Hire performs this maneuver in the second New Avengers #1. Victoria Hand (Token Good Teammate of the Dark Avengers) meets him at the Avengers Mansion because Captain America (comics) asked her to, but shows up with a gun on the grounds that she has no powers to defend herself with and the Avengers aren't exactly fond of her. Since he has Jessica and their baby with him, Cage demonstrates that the gun isn't much help by clapping his hands together so hard Hand goes flying.
Superman has been known to do this on occasion.
In JLA: Incarnations #5, Vibe and his vibrational powers show you how it's done.
Flint did a more narrow-focused version of this technique during her time with Stormwatch Red.
In X-Men The mutant Arclight, in addition to her superhuman strength, endurance, and durability, has the ability to create seismic energy with her hands that generate shockwaves and geo tremors. As noted below, her film incarnation possesses the same abilities.
In his first appearance, Lightning Lad of the Legion of Super-Heroes had his Shock and Awe powers work this way (it was later changed to just using lightning without any clapping). From the story itself:

Lightning Lad: "My hands are like the positive and negative poles of a battery! Each time I clap them together, a super-lightning flash leaps forth!"

Film

X-Men: The Last Stand: a villain called Arclight (see above) has this ability. And that's all she does, but apparently she can control it well enough to make sure the shockwave only breaks certain materials.
Also used in The Incredible Hulk movie by the titular character to douse a fire.

Literature

In Sir Thursday, Dame Primus does this with the Second Key, which takes the form of a pair of gloves.

Tabletop Games

An addition to the Super Strength power in Mutants and Masterminds.
One of the psychic powers (called Thunderclap) available to Space Wolf Rune Priests in Warhammer 40,000.
The Thunderclap feat in Dungeons and Dragons 3.5. Mostly reserved for monsters because of its insane 30 Strength prerequisite.

Video Games

City of Heroes: The Hand Clap power from the Super Strength powerset.
- Some of the electrical themed power sets also receive Lightning Clap, which is functionally identical.
Champions Online: Thunder Clap from the Might framework.
DC Universe Online: Might characters can clap their hands to create a very focused, damaging ranged shockwave.
One of the central game mechanics of Donkey Kong Jungle Beat. It would later be brought over to Super Smash Bros. Brawl in the form of Donkey Kong's Final Smash.
In Marvel Super Heroes and subsequent Marvel vs. Capcom titles, this is Hulk's heavy air attack.
Alex Mercer. That is, when he's not just eating people.
- Even better, he's not clapping hands. He's smashing his knuckles together.
The Thunder Clap ability, from the Mountain King in Warcraft III and the Pandaren Brewmaster in Defense of the Ancients.
Colossus from X-Men Legends.
In Mortal Kombat: Deadly Alliance and Armageddon, Hsu Hao has a special named "Khan Klap/Thunder Klap" (note the intentional misspelling) which emits a visible pulse of air that damages his enemy while pushing them back.

Web Comic

Captain Excelsior: The Thunderclap.

Western Animation

In the second season of the Fantastic Four cartoon, the Hulk knocked Johnny out of the air this way.
In Megas XLR, the Humongous Mecha does this in the first episode.
Fourarms does this a lot on Ben 10.
Transformers Animated: Bulkhead does the shockwave part unintentionally.
The Stone Giants from Disney's Atlantis the Lost Empire actually generate force fields by clapping their hands.
Johnny Test has this ability when he (thanks to one of his sisters' lab experiments) turns into Johnny X. He calls it his Hurricane Hands.
In Superman the Animated Series, Supes puts out a burning apartment this way.