Just got thinking about it. As far as I recall, the Spaniars brought a lot of gold and silver from Central and South America. I believe (perhaps wrongly) that if something like that happened today (a relatively sudden entry of large amounts of precious metals to the market) the economy would be greatly affected, even if it isn't so tied to gold and silver these days.
This is a very interesting question, and its answer leads to some of the conclusions that brought about the ideas of modern economics. Much of it belongs in an economic, rather than historical, discussion, and I'm afraid any speculation about the modern effects of a sudden bullion influx would break this sub's 20-year rule. Nevertheless, there is still some historical insight to be had here.
First, it is important to remember that the economic system Spain followed for most of its colonial period was mercantilism. Indeed, the study of economics as we understand it simply did not exist. What this means is that the crown was simply focused on getting as much gold as possible by getting control of as much land and as many trade routes as possible. Spain was extremely successful in this regard, as you can see from the table below, which provides the total amount of bullion imported into Spain (in pesos) from 1503 to 1660^1*.
| Period | Public | Private | Total |
|---|---|---|---|
| 1503-1510 | 75,176.30 | 211,756.20 | 286,932.50 |
| 1511-1520 | 114,690.50 | 323,059.40 | 437,749.90 |
| 1521-1530 | 61,444.60 | 173,076.60 | 234,521.20 |
| 1531-1540 | 356,649.10 | 760,975.70 | 1,117,624.90 |
| 1541-1550 | 470,092.00 | 1,622,451.20 | 2,092,543.20 |
| 1551-1560 | 1,039,400.40 | 2,533,505.50 | 3,572,905.90 |
| 1561-1570 | 1,120,855.20 | 3,948,895.00 | 5,069,750.20 |
| 1571-1580 | 1,989,667.80 | 3,842,042.20 | 5,831,710.00 |
| 1581-1590 | 3,118,763.30 | 7,522,685.20 | 10,641,448.50 |
| 1591-1600 | 4,199,533.30 | 9,723,139.30 | 13,922,672.60 |
| 1601-1610 | 3,013,912.90 | 8,147,794.10 | 11,161,707.00 |
| 1611-1620 | 2,312,141.90 | 8,615,974.20 | 10,928,116.10 |
| 1621-1630 | 1,901,991.40 | 8,491,049.60 | 10,393,041.00 |
| 1631-1640 | 1,885,025.50 | 4,800,065.70 | 6,685,091.20 |
| 1641-1650 | 1,261,754.90 | 3,845,115.00 | 5,106,869.90 |
| 1651-1660 | 569,080.40 | 1,561,896.10 | 2,130,976.50 |
Essentially, Spaniards began to buy goods with this imported treasure instead of making goods themselves. As others have pointed out, this led to a fairly predictable result: prices rose (inflation), and Spain began to import far more than it exported. Again from Hamilton, "the importation of treasure ... in exchange for goods sapped the economic vitality of the country and augmented the price revolution, which handicapped export industry." In essence, Spain simply stopped making as many exportable goods as it should have, meaning that bullion from the Americas was a main source of its wealth. Instead of getting wealthy by making something, young Spaniards were getting wealthy by finding bullion. This allowed industries such as textiles in Britain to flourish while Spanish industry faltered.
Now, this is where the interesting observations on the nature of mercantilism come into play. The Spanish crown acted as any good mercantilist would, began to take much of this gold for itself. All told, about 25% of gold coming into Spain went straight to the crown^2. Instead of being invested in things like production and Spanish business, it went toward military ventures, some across Europe, but mostly as protection for existing mines and the ships bringing gold across the Atlantic. Similarly, a large portion of the gold went simply toward making sure non-Spaniards didn't have access to Spanish mines and Spanish gold. Another large portion went toward expanding Spanish holdings in the Americas (of course leading to the discovery of yet more gold). Unfortunately for Spain in the long run, their empire simply got too big, and the Spanish government stopped being able to sufficiently monitor Spanish mines. Enterprising individuals could avoid paying taxes relatively easily by simply walking out of Spanish lands with their gold, so smuggling became an important issue. It did not help that the Hapsburgs had a nasty habit of focusing military strength on Europe, rather than the Americas during this period^2.
Spain inevitably began to lose lands to other European powers, gold and silver mines began to dry up, and enough people figured out how to avoid paying Spanish taxes. The result of this perfectly exhibits mercantilism's ultimate failure: once Spain ran out of gold, people stopped having a reason to trade with Spain. Spain steadily lost both power and money, and its empire largely ceased to exist in the early nineteenth century.
tl;dr: The massive importation of American bullion into Spain caused inflation, effecting a drop in Spanish exports and an increase in Spanish imports. Spanish workers stopped making anything worth exporting, and when profits from American gold began to fall, so did the Spanish Empire.
If you're looking for an overview of the economic effects of colonialism on Europe, my second source is a good start.
^1. Hamilton EJ. Imports of American Gold and Silver Into Spain, 1503 - 1660. The Quarterly Journal of Economics. Vol. 43(3) pp 436-472. 1929.
^2. O'Brien PK, De La Escosura LP. The Costs and Benefits for Europeans from their Empires Overseas. _ Revista de Historia Económica - Journal of Iberian and Latin American Economic History_. Vol. 16(1) pp. 29-89. 1998.
* I'll just leave the original author's description of what a "peso" means here:
In this case peso means 450 maravedis' worth of gold or silver. It was equivalent to 652.635 grains of pure silver until December 23, 1642, when its "silver content" was reduced to 522.09 grains. Peso also had various other meanings, a good account of which can be found in Haring, "American Gold and Silver Production in the First Half of the Sixteenth Century," Quarterly Journal of Economics, xxix, 476-479.
Edit: Clarification on the table
My economic history teacher basically said that it led to inflation in Spain, made it harder for the Spanish textile industry and other export oriented industries. This meant that it became cheaper for Spaniards to buy goods from other countries, thus spending more on imports. Another problem was the lack of investments in Spanish industry, as much of the gold and silver was used on consumables and luxury.
One consequense of this, was that British textile industry, which at the time was less advanced, started to flourish.
This is just the basic idea of how the gold and silver gave an impact on Spain. A lot of the gold and silver left Spain due to their larger reliance on imports, and about 15 % of it never even got to Spain due to piracy, storms, etc.