In much of the Known Lands, currency has been standardized ever since the times of the Atalan Empire - thanks to rituals and magic items which could identify whether gold, silver, and copper coins meet certain minimum weight and purity standards specified by the Atalan Emperors. These magics are still in widespread use, and ensured that even governments separated by large distances minted coins which are basically interchangeable in economic transactions. Thus amount of money in circulation basically depended on the availability of the metals used for minting the coins, and thus determined the relative wealth of individuals or governments possessing them.
However, with the recent rise of large-scale trade and commerce, and more importantly the establishment of large regional and interregional banking systems, a new form of money has established itself: Bank notes.
Bank notes are issues by large banks and come in a variety of denominations depending on the bank issuing them. These notes can be redeemed at the bank issuing them for a number of gold coins depending on the type of note. Typical denominations are 5, 10, 20, 50, and 100 gp, and larger banks offer notes worth 200, 500, or even 1000 gp. Larger denominations are known, but are only printed for special occasions and are practically unique. As far as it is known, bank note with the highest denomination was printed by the Gemeinschaftsbank and was worth 1,000,000 gp - though rumors of even higher denominations persist.
Bank notes are printed showing their denominations, the symbols of the bank issuing them, a signature of the chairman of the bank, and all sorts of artistic details which make the note harder to forge. Each bank uses its own special paper for its notes whose precise production is a closely guarded secret. For the higher denominations, certain enchantments which make the note even harder to copy are woven into the paper as well.
All this combines to make bank notes as well-established as money as regular coins, and in most cases notes are accepted as money in places where the bank issuing them has established itself without any question. Nevertheless, attempts to forge notes are made by enterprising criminals from time to time. The banks alway spend considerable resources to bring these forgers to justice, as it undermines the trust their customers have in the bank.
While the general public is unaware of this, it is no secret in financial circles that most banks tend to issue significantly more notes than they have gold reserves. In the case of the largest and most well-established banks, such as the Gemeinschaftsbank, this can be as much as several times the amount of gold they have in their vaults. Needless to say, this has increased the fortune of the banks by enormous amounts.
This system works as long as most owners of bank notes accept the notes as money instead demanding that they should be exchanged for gold. And indeed, the largest banks have cultivated an image as being utterly trustworthy and dependable that the odds of this happening are very low. Smaller banks must be more careful - if there are too many rumors of fraud, embezzlement, low gold reserves or just a too speedy issuing of new notes, a rush of nervous customers might demand that their notes are exchanged for gold, and if the bank finds itself unable to honor those claims, it will find itself bankrupt and its leaders pursued by the law.
Most banks care careful not to issue too many notes too fast - they know that these notes are only worth something as long as they can cultivate an image for trustworthiness. The oldest banks have become very good at this, and have used their printed money to give credits to many people and organizations, which has been one of the foundations of the current economic growth in many regions.
Some governments have also attempted to issue their own notes, but this has only been met with mixed success. These notes are only worth much in places where the government issuing them holds sway, which in most cases is a far smaller region than those of the larger banks. Furthermore, since governments (unlike banks) can force their citizens to accept these notes as legal tender, they are often tempted to print far more notes than their economy can support, resulting in inflated prices and a black economy where these notes are traded at values vastly below their printed denominations (while "legit" businesses find all sorts of excuses not to use these notes at all).
The largest-scale attempts at government-issued paper currency can be found in the Alliance of the Pantheon and the League of Armach. The trust in these notes are fairly brittle. While most patriotic citizens of the Alliance accept the notes, many observers feel that this won't last long if the Alliance should suffer any military setbacks. The League of Armach, on the other hand, suffers from inflation as the government is eager to print new notes to pay for its military expenditures. It doesn't help that both governments secretly print forged notes of the other nation in order to damage the other one's economy.
Both Narevoreen and the Hobgoblin Dominions also have region-wide systems of paper currency, though such notes are not yet in widespread circulation. The Tsan Empire, on the other hand, has an old and established system of paper currency (in fact, it might be the oldest in the world) - though it is based on units of jade instead of gold.
Adventure Ideas
Designer's Notes & Resources
From a game perspective, bank notes exist to make transporting money more convenient for the player characters. If the characters end up becoming wealthy - not an uncommon occurrence in most campaigns - they do not have to carry hundreds of pounds of gold pieces with them if they want their wealth in portable form, as a bundle of notes from the Gemeinschaftsbank will do just as well.
To be sure, not all bank notes will be accepted everywhere, but since much of the setting is urbanized and civilized, this should not usually be a problem. For the sake of convenience, the GM should assume that the characters have informed themselves in advance what kinds of notes they can use in the places they plan to visit and thus carry notes from the right banks. If they plan to visit a region where no banks are available (such as remote rural areas, or regions in the far South or East of the Known Lands), he should inform them in advance so that they can stock up on gold instead.
Additionally, the information about the possibility of a banking crisis is not provided so that the GM can arbitrarily take away large portions of the wealth of the characters, as this will only cause resentment among the players and distrust of a system that is supposed to help the characters, not hinder them. Instead, it should be seen as a springboard for adventures - most banks are ruthless about protecting their image, and the plots involved in either saving or destroying the reputation of a bank can provide fodder for entire campaign arcs.