In Speed Grapher, Suitengu smokes cigarettes wrapped in 10,000 Yen bills. Even worse, he crushes them underfoot after no more than four drags, then lights another in less than a minute. If that's not enough, at one point he nonchalantly sets fire to a whole briefcase worth of the bills. And then takes it to the most extreme, when he torches every last yen Japan has in a skyscraper.
Joker: It's not about money. It's about sending a message. Everything burns.
Brazilian movie O Homem Que Copiava (The Man Who Copied) opens with the protagonist burning money - though it probably is In Medias Res, as the story has him using a photocopier to make money, and later regretting it.
In Thank You For Smoking, when the original Marlboro Man threatens to sue the tobacco industry, Nick Nailer comes by with a Briefcase Full of Money. However, he doesn't accept the bribe. Nick then suggests that he go to the press, tell them that the industry offered you all this money, then dump it out of the briefcase and set it on fire. The Marlboro man then sheepishly suggests that he just burn half of the money - but Nick then tells him that it's an all-or-nothing deal. He then accepts the bribe, like Nick knew he would.
Used justifiably in Cliffhanger when Gabe burns some of the stolen money to keep himself and Jessie warm. The bills were headed for destruction by the Treasury anyways.
In Fast Five, Toretto and his crew use this as part of a Batman Gambit. They set one collection (around ten million) of Reyes' money on fire, so that he will move all of the rest to one location that they can then steal all at once.
In Agatha Christie's short story "The Soul of the Croupier", the Countess does this to the high denomination bill that the croupier arranged for her to win, because she will not accept his charity. He is her long-estranged husband.
American Psycho: One of Pat Bateman's friends teases a homeless guy with a dollar bill and then lights his cigar with it. Pat thinks he's a jerk but it's not worth killing him over— he likes the homeless even less and kills one later.
In Spider Robinson's Callahan's Legacy, a character who inherited a frickload of money decides to "combat inflation". He and his friends fold the bills into paper airplanes and send them flying into the fireplace.
At the beginning of Terry Pratchett's pre-Discworld book Strata, protagonist Kin Arad is uninterested in Jago Jalo's claims of an uncharted world where thought becomes matter, until he takes out a couple hundred thousand years worth of the life-extension tickets that function as the setting's currency and casually tosses them all into a trash disintegrator.
In Fyodor Dostoevsky’s The Idiot, Natasya Filipponva heard that Gavrila Ardalionovich would “crawl to Vassilievsky Island for three roubles”. She tests Gavrila by throwing a packet of ten thousand roubles into a fire, and telling him that if he reaches in with his bare hands, he can keep whatever he grabs.
Lazarus Long does this to a big bill in Time Enough for Love after his bank gets nationalized. He's trying to teach the mayor that money is a fiction and he shouldn't get too attached to the notes themselves. Lazarus then comments that that's what he usually does when the safe starts to get too full. Then he writes down the serial number so he can keep track of the currency in the system.
Live Action TV
In the shortlived sitcom Paris, one character does this, saying, "What's fifty francs to a man like me?". When told it's a one-hundred note, he promptly stamps it out, complaining that no one had told him.
Jonathan did this during his supervillain period on Buffy the Vampire Slayer. It heralded his eventual death of course, since everyone on the show who smokes ends up dead.
All the disrespect, none of the flame: at the end of The Three Stooges 'Sing a Song of Six Pants', they're rummaging through a wad of $100 bills. Shemp comes across a $50, crumples it, and tosses it aside saying 'How'd that get in there?' The others wave it aside. Then they come to their senses.
Fr. Buzz: 400 dollars?? You know what I do with $400? I wipe my ass with it.
Father Ted: Good God. And can that still be used as legal tender?
Season two of The Wire: Ziggy Sobotka celebrates his having earned some money under the table by lighting his cigarette with a burning $100 bill. This isn't even the dumbest thing he does.
When Harry Enfield's Loadsamoney character appeared on Comic Relief, he sold someone a red nose for £5 (at the time the retail price was 50p), then blew his nose with the fiver and threw it away. He immediately got hit by a car.
One of the "bonus rounds" in the UK version of Distraction awards the contestant £5000 for winning the game - then for every question he gets wrong in this round, he must throw £1000 of it onto a wildly burning fire, where it must stay until the end of the round. A similar game is played with the money in toasters.
In one episode of Person of Interest Reese intercepts a mook carrying a duffel bag full of cash that was intended as a payoff for some dirty cops. He wants the mook to give him information about a murder and to show that he is serious he starts burning the money. The mook panics since his boss would never believe that someone was willing to just burn so much money. He would just assume that the mook stole the money and have the mook killed. With no other choice he tells Reese everything he knows.
On an episode of The Wild Wild West, Diabolical Mastermind Dr. Loveless burns the proceeds of his bank robberies on a bonfire to prove a point to his men, but one of them sneaks one of the hundred-dollar bills away and it falls into the hands of West and Gordon and puts them on the robbers' trail. When Dr. Loveless finally gets the bill back, he lights it on fire, then uses it to light his cigar.
Burn Notice: In "Friends and Enemies", a lawyer who has been marked for death by a biker gang offers the bikers all of the money he has in the world. One of the bikers empties the bag of cash onto the lawn and sets fire to it to show that this isn't about the money.
Season three of Breaking Bad opens with Walt piling his drug money on the barbecue, as getting it has cost him his morals, his relationship with his wife and caused hundreds of deaths. He chokes halfway through and throws it into the pool.
One episode of Hogan's Heroes has the Nazis set up a printing press inside the camp to make counterfeit money and wreck the Allied economies. After they destroy the press, the Heroes find that Schultz kept some of the money for himself, and Hogan sets it on fire with a cheerful "Always wanted to have money to burn" while poor Schultz looks on.
In the Red Dwarf episode Marooned, Lister and Rimmer are looking for kindling to keep the fire going. Once all the books have been burnt, Lister burns the 24 grand that Rimmer has saved up. To be fair, Rimmer is dead already and has no use for the money and even if he did, there is no civilisation left in which to spend it.
The Dukes of Hazzard had an episode where Boss Hogg made a deal with an elderly woman where she would get half the money up front - but Boss' idea of half was to chop the bills in half with a paper cutter. To get Boss to give up the rest of the money, Luke set the woman's half on fire, which would make Boss' half worthless. He relents, saying "Burning money is against my religion."
The music video "Beautiful Dirty Rich" by Lady Gaga has her doing this with some rolled up bills as them being the cigar. Also just burns a 100 as well.
In the video for "This is the Life", a filthy rich "Weird Al" Yankovic lights a cigar with a 100 dollar bill.
The video for Superdrag's "Sucked Out" ends with the lead singer lighting a cigarette with a $1 bill. Given the tone of the song to which the image is attached, this was likely meant to be symbolic.
Accidentally happens in The Unsinkable Molly Brown. When Johnny leaves Molly $300,000 in cash as a wedding present, she considers where in the cabin it could be hidden where a robber wouldn't think of looking for it. She decides to hide it in the stove, underneath some kindling. When Johnny comes home shivering, the first thing he does is light the stove.
In Dead Rising 2, one casino features a "Game" called "Money to burn" that is quite literally a bonfire that you throw increasingly large amounts of money into for Prestige Points (experience). After you do it enough times, you are given a "Stupidity Bonus".
Fallout: New Vegas has a variation, where Legion denarius can be used to create "coin shot" rounds for certain shotguns.
Before that was Fallout 3's Bottlecap Mine, a craftable explosive weapon that uses bottlecaps, the series' usual in-game currency, as shrapnel. The head of a caravan company in New Vegas lampshades this, wondering why someone would actually want to waste money in this manner.
In The Simpsons, Krusty lights a cigar with a $100 bill. Okay. Then he lights another with a pearl necklace, and later another one with a copy of Action Comics #1.
Alternatively parodied when Homer lights up a $5 bill to smoke a cigar to demonstrate his potential investment earnings. Then he realizes he's burning money, quickly extinguishes it, and adds it to the similarly singed bills already in his wallet.
In the episode "Chocolate With Nuts", Squidward's Fancy Living Magazine features a High-Class Glass Fish burning a dollar, because he can!
In another episode, Spongebob and Patrick try to prank Mr. Krabs by burning a dollar, but he throws a bucket of water on it and the pranksters are revealed.
In "Pretty Patties", Spongebob and Patrick have no idea what to do with their fortune. Burying, shredding, and burning actually took too long! So they just gave it right back to their customers in large bags.
Title of a 1980s episode of G.I. Joe, in which Cobra burns United States of America money.
Parodied by Futurama's Le Grand Cigar. Its wrapper was a piece of the original U.S. Constitution. It was hand-rolled by Queen Elizabeth during her "wild years" and was buried with George Burns until grave robbing space mushrooms stole it. Bender then decided to steal it rather than pay its $10,000 cost.
Archer has Cheryl, the ditzy secretary, turn out to be the heiress of a family that made its fortune on the railroads. Once she comes into her inheritance, though, she won't pay back Cyril the $3000 he lent her because "that money doesn't exist anymore" - because she set it on fire to watch it burn.
Walter Lantz once made a version of the Elves and the Shoemaker where the shoemaker, after the elves helped him, became so wealthy he set a bill on fire to light some candles.
Played with in Family Guy when Carter literally blends $20,000 and drinks the smoothie instead of giving to Joe's Charity.
Earlier, the K Foundation had set up a cash prize to award to "the worst artist of the year". Their shortlist was identical to that of the Turner Prize, which was going on at the same time. Amanda Whitehead won both the Turner Prize and the K Foundation's award. She refused the latter "prize", at which point the K Foundation threatened to set fire to the cash. Whitehead prevented the burning by accepting the prize at the last minute, stating that she would donate the money to charity.
A justified example: Germany's economy was destroyed after World War I, resulting in hyperinflation to the point that Marks were more useful for papering bare walls than using as currency. It got so bad that the bills were worth less than what they could buy in firewood. There were also more German bills in the United States than in Germany, due to them being sold to Americans as novelty pieces.
This is also true in places like Somalia, where the money is so worthless people need a wheelbarrow-load of it just to buy apples or bread. Most people just use the money for animal bedding or toilet paper.
Hyperinflation in general tends to cause this, as the paper money is LITERALLY worth less than virtually any other substitute.
One odd example during this period came from the practice of producing "notgeld" (emergency money) by town governments, local banks, and other sources not officially authorized to issue money. Notgeld wasn't actually legal tender, but within the locality it would be interchangeable with real money. Some notgeld pieces are now quite rare because the unusual materials they were made from left them especially suitable to burning as fuel once the emergency passed and non-inflated real currency (which the notgeld could no longer be exchanged for) was available. These include notes made from thin planks of wood instead of paper, and coins made from pressed coal dust. Once the hyperinflation period passed, most of these wood banknotes were tossed into fireplaces, and the coal coins were tossed into stoves.
This is parodied in Astérix, where pearls dissolved in vinegar are Cleo's favourite drink.
Serge Gainsbourg famously burnt a 500 franc bill on TV at the height of his fame.
Back in the 1970s, poker player "Mad Genius" Mike Caro would get inside his opponents' heads by burning a $100 bill before playing a single hand, just to make everybody there think that money meant absolutely nothing to him.
The Aztec civilization used cocoa beans as one of its sources of currency. So when the rich and powerful drank chocolate...
A popular chemistry demonstration subverts this by soaking a banknote in aqueous isopropanol and setting it alight. If you've got the composition right, the note survives unharmed. The trick is that isopropanol burns with a bright but not particularly hot flame, and the water keeps the paper itself below its ignition temperature.