Cacophony Cover-Up

Loud noises... Sometimes you make being a ninja so easy.

—The Adventures of Dr. McNinja

You've got to do something stealthily. The problem is, the thing you want to do is going to make a lot of noise, and you cannot silence it in any way.

What to do? Drown it out with a bigger noise. You can create it yourself, or just wait until something loud happens nearby and make your move then.

This follows the same logic as Needle in a Stack of Needles, Lost in a Crowd, and I Am Spartacus, except those are covering up objects and people, not actions.

Examples of Cacophony Cover-Up include:

Anime and Manga

Lupin III used a fake construction crew to cover the sound of his other goons breaking into a vault.
In Higurashi no Naku Koro ni, the Yamainu use the cover of festival fireworks to conceal the noise of exploding their way into the Sonozaki bunker.

Film

The Shawshank Redemption: Andy Dufresne uses thunder to drown out his banging on the pipes with a rock, to break through them in order to escape.
Happens unintentionally in Indiana Jones and the Last Crusade, when Indiana smashes a hole in the floor of a library in time with a librarian stamping books.
- Used straight in Temple of Doom, when one of Lao Che's goons shoots Indy's accomplice when champagne bottles are being popped open.
Referenced in Mission: Impossible 2: "The generators will cover the sound of Hunt's break in".
- Nyah's theft of the necklace early in the movie involves a similar trick. To cover the sound of her high heels as she runs to the room where the necklace is kept, she only runs while dancers downstairs are dancing, making their own heels-on-floor noise.
In one of the most famous heists of the Olsen-Banden (Olsen's Gang) series, Olsen and his gang performs a daring breakin of the Royal Opera during a performance of the danish classic, Elverhoj. They have to break through several sealed doors to get where they're going, and carefully time every action to coincide with appropriate musical cover. (Setting off dynamite charges during cymbal clashes, running concrete-drills during woodwind sections, ect.)
In The Man Who Knew Too Much there is an attempted assassination during a concert, using a cymbal crash to cover the sound of the gunshot.
In the movie A Shot in the Dark, an attempt at murder is made at a nightclub during a flamenco dance, with the gunshot being timed to coincide with the dancer's boot tap.
In Entrapment a clock's chimes are used to mask the sounds of breaking in.
In The Departed, one gangster is shown out in the street, tossing cherry-bombs, apparently for fun. We realize in the next scene that he was covering for the sounds of gunfire.
In The Great Escape, they do this at least twice. Once, with singing "Twelve days before Christmas". When starting the tunnel and needing to break a thick piece of slate, some of the prisoners pound some stakes into the ground with mallets (for their vegetable gardens that are part of the distraction as well).
Used straight in the film of Enemy at the Gates in Vasily Zaytzev's Establishing Character Moment where he dispatches five Germans with five shots purposefully timed to coincide with bomb explosions.

Literature

Frank Garcia's Marked Cards and Loaded Dice had a story attributed to John Philip Quinn, a 19th century crooked gambler. One day a man approached Quinn and asked to become a "bottom dealer" for him. As the man dealt out the cards Quinn listened for the distinctive sound of a poorly executed bottom deal. He then told the man that if he would give Quinn a signal when he was about to begin, Quinn would fire off a pistol and distract everyone else in the room from the horrible noise the man made.
Marie Brennan's Doppelganger duology has Mirei, newly restored to her original body by the Fusion Dance of Miryo and Mirage, using the cover of applause to knock out a pair of guards and confront the Primes.
In A Stainless Steel Rat Is Born, the main character bases his plan for a concert hall burglary around the musical compisition to be played, so that the noisiest parts of the job take place during the noisiest part of the concert.
Overlaps with We Need a Distraction in Death or Glory. To cover up the sound of most of their team cutting into an ork encampment with a laser torch, they make a huge ruckus at the main gate -- with a rocket launcher.

Live Action TV

The pilot episode of the Mission: Impossible TV series uses fireworks to cover the sounds of the team's escape. (I think, it may have been something else they were covering.)
This is used in Farscape when John is hiding in the walls from the bad guys who can hear his heartbeat and breathing. His shipmates start speaking loudly in various alien languages to give him time to escape.
A minor Running Gag in The A-Team is that whenever Face and Hannibal were captured, their friends would naturally come to rescue them. When they realized their teammates were close by, they would cover up their noises by singing "You Are My Sunshine."

Video Games

In Splinter Cell: Chaos Theory, you can get away with making noise if the ambient sounds of the environment are loud enough.
One of the first puzzles in Zork: Grand Inquisitor requires you to turn the propaganda-spewing speakers' volume to maximum, so that you can steal something from a shop without the owner hearing the alarm bell.
One of the final puzzles in Still Life 2 requires you to turn on a large fan while you sneak up on the villain.
One of the main story assassinations in Assassin's Creed II could be accomplished using Ezio's pistol, if you timed your shot with the fireworks going off in the area.
Battlefield: Bad Company 2: Similar to the Assassin's Creed II example, a storyline mission sees you providing sniper fire support at night with a huge thunderstorm right overhead as the rest of your fireteam sneaks into an enemy camp. In order to avoid alerting the guards to your shots, you time them to coincide with the sounds of the storm.

Web Comics

In The Adventures of Dr. McNinja, the doctor has to blow up an entrance into a truck, so he has his friend drive by in a car playing very loud music to cover up the explosion sound.

Western Animation

In a King of the Hill episode, Strickland and the other local propane shops start an illegal price-fixing racket and Hank is forced by the Feds to wear a wire during one of their meetings so that the team assigned to catch them could have proof. So how does Hank keep from getting Strickland shut down? He gets the freaking Orange County Choppers to rev their engines outside the store in order to cover up his explanation of the situation to Buck.

Real Life

Car stereo thieves sometimes intentionally trigger a nearby car alarm to mask the sound of breaking glass.