Hear Me the Money

"I know that sound, and I love it"!

—Marcus Lycus, A Funny Thing Happened on the Way to the Forum

When receiving a payment, a character takes a stack of money (or a case of coins) to their ear and flips through it, to hear whether or not all the money they were promised was there.

Could be Justified: since the paper they print money on is special paper, the sound it makes while flipping might be different than counterfeit bills printed on regular paper. And with coins, various densities and shapes could also make different sounds.

Anime and Manga

Spice and Wolf has an instance that falls somewhere between this and Tasty Gold. Holo is able to judge the purity of coins just by clinking them together, leading to the plot point that a city is minting coins that have a lower silver content and are thus worth less.

Comic Books

Scrooge McDuck has done it on occasion obviously, and in one story (don't ask me the title) Donald Duck is shown to have inherited the talent as well. (Being Donald of course, it soon turns out that it's no use if he has Scrooge's talents if he doesn't have his skills and work ethic as well.)

Film

During Austin Powers's final confrontation with Dr. Evil in the first film, in a deleted scene, Number 2 attempts to bribe Austin with $1 billion in a Fendi briefcase. When Austin grabs just one stack of $100 bills, he notes that the money is short of a billion, to which Number 2 mentions the Fendi briefcase being part of it. They continue to argue until Dr. Evil presses the button to eliminate Number 2. Of course, Austin could have told that the money is short of a billion by the simple fact that you can't fit ten million $100 bills in a single briefcase.
The 1989 film Who's Harry Crumb? with the late John Candy has this, Double Subverted. When he comes upon one stack of bills that he says is short by one, another character rolls her eyes and insists it's insane to think he could know that just by flipping through it. They count out the bills by hand, and sure enough, there's one bill missing.

Literature

In Hogfather, the Auditors of Reality leave a rather unusual payment when they commission the Assassin's Guild to off the eponymous holiday figure: blank discs of pure gold. The head of the guild bounces one on his desk, and the sound and bounce of the "coin" confirm its composition for him.

Live-Action TV

In 'Allo 'Allo!, the rich but rather miserly Monsieur Alfonse is able count the money which is owed him like this. He's good enough to detect the absence of a single, solitary note - at one point, he looks about ready to accuse René of cheating him until René reaches into the box and produces one that had come loose from the sheaf.
On Good Times, pimptastic crime lord Sweet Daddy does this to a stack of money he seized from his lieutenant, Bad News. This is because of a lack of trust in Bad News, who tried to bribe JJ into not giving Sweet Daddy a life-saving blood transfusion, so he could take over Sweet Daddy's operation.
At least one episode of the 1950s adaptation of Blondie showed that Dagwood can do this, which perhaps helps explain why Mr. Dithers hasn't permanently fired him. He riffled a packet of bills beside his ear, made sounds like an adding machine, and then announced a cash value with over-the-top precision.

Tabletop Games

In the Complete Book of Villains, a 2E Dungeons & Dragons supplement, a dragon is presented as an archetypical villain representing greed. When its minions bring it tribute, it listens to the coins being poured out onto its hoard, and immediately detects from the sound that one of them has cheated it.

Western Animation

Batman: The Animated Series had this in "The Strange Secret of Bruce Wayne". The thug thumbing the money to his ears was appropriately named "Numbers".
South Park episode "Super Phun Time" has a combination of this and subversion of Tasty Gold. Robbers had stolen both money and food from a Burger King. When one of them wants out, he is given his cut. He then flips through the sandwich to make sure that all of the toppings were there.

Real Life

Newcastle, Australia's local radio station KOFM used to have a contest where they would play the sound of flipping notes and you won the money if you could tell them how many notes they had just flipped. A few people won, so possibly there's a grain of truth. Or people are just good at guessing.
A variation: the most famous folktale about the wise Japanese judge Ooka Tadasuke is about a restaurant owner suing a poor man for payment. The poor man would eat his daily meal of plain rice near the restaurant so he could smell the food cooking, which made his rice taste better; when the owner discovered this, he sued for payment, and judge Ooka found in favor of the restaurant owner. The poor man protested, saying he only had enough money for rent, showing the judge the few coins he had. Judge Ooka had the poor man pour the coins from one hand to the other a few times, and then told him he was free to go. When the restaurant owner said he hadn't been paid yet, judge Ooka informed him that he had just been paid—the price of the smell of food is the sound of money.
- This is a common folktale that has been recast for many different cultures and peoples.