Stage Money

To create the illusion of massive wads of cash, TV and film producers don't take real $100 bills and put them on the front and back of a stack of $1 bills (or even just pieces of paper cut to size) but instead use fake bills.

This is also seen any time where the character shows a bunch of bills. Rather than going to the bank and getting, say $5,000 in real money, letting the actor use it for the scene and then putting in back in the bank, they use Stage Money.

There's actually a cottage industry that makes fake money to be used in films, that looks just enough like the real thing that a casual viewing doesn't reveal that they're fake... for one example, take a look here. Users of Poser software can freely download U.S. money props, including various coins and four different currency styles. The 20th century bill props are not intended to imitate genuine currency.

It isn't legal for print media to use real money, to the point that boxers with accurately sized money on it were once seized. So the magazine ad would show part of a hundred dollar bill, but not all of it. Because the law says that only the government can print money. There is no law against showing it on TV or in the movies, since you can't cut out the bills and use them.

In Britain, if a TV game show has a prize draw with cash prizes and illustrates them, the £10, £20 or £50 notes will be shown in full but with something like "SPECIMEN" superimposed. In some other parts of the world, bank notes illustrated in print media (such as ads) often also have that SPECIMEN marking.

Examples of Stage Money include:

Film

The setting of the 2005 adaptation of Charlie and the Chocolate Factory was designed to look like America to Britons and like Britain to Americans, made use of "guinea" notes that didn't look quite like either a $10 bill or a £10 note.
One short from The Three Stooges has them needing to get the ransom for a starlet. They resort to some bills found in a room marked 'Property'. It didn't say whose property, of course. Guess what the roll was identified by the crooks as...

Literature

In Making Money, the Ankh-Morpork Times broke the story of Moist von Lipwig's new invention, paper currency, by averting this trope. They printed true-to-scale images of the front and back of a bank note, which (as Vetinari observes) surely sent most of the city scrambling for scissors and glue.

Live-Action TV

Doctor Who had some specially commissioned notes made with portraits of David Tennant and (producer) Phil Collinson on them for The Christmas Invasion. This was for legal reasons, though, and now these props go for a pretty penny on eBay.
- The reason Doctor Who used fake notes may have been not so much that they weren't allowed to use real currency, but that the scene involved a cash machine malfunctioning and shooting banknotes across the street. There'd be too much risk of the notes becoming damaged or getting pocketed by the extras who scrabble across the street collecting the notes. It's not an offence to show currency on British TV, but it is an offence to damage or destroy it.
Notably averted in Art Attack, where Neil Buchanan made a vast portrait of the queen out of hundreds of thousands of pounds worth of real £10 notes, which the Bank of England lent him.
On the NBC game show Scrabble, players could earn bonus cash by placing letters in colored squares on the gameboard and then immediately guessing the word in play. Host Chuck Woolery would then pay out the bonus in pink or blue "Chuck Bucks," fake bills printed with his picture.

Music

Harry Enfield's early character Loadsamoney's "wad" used the first method described above, being two real £10 notes with lots of appropriately cut newspaper in between.

Theatre

The Stephen Sondheim musical Road Show involved piles of cash being literally thrown into the air until they carpeted the stage, so that audience members in the front few rows were able to catch loose bills. Needless to say, it wasn't real money.

Real Life

Real Life example: During the Victorian era, forging a banknote carried a hefty sentence, but making something that looked a bit like a banknote didn't. So forgers would create notes that read "Bank of Engraving" instead of "Bank of England", and could try to pass these off as real currency.
To someone who goes to Chinatown often enough, it's obvious when someone is using Chinese Hell dollars as stand-ins for American dollars, but otherwise the designs are quite similar. This troper has seen them used like that in an episode of the Australian series Pizza.
A related trick in real life: the "carnie roll", a roll of what appears to be high-denomination bills. The first and last ones are, all the others are $1 bills.