In terms of impact, the influx of precious metals into Spain (and then to the rest of Europe) from South America from the late 15th to the 16th century is hard to match. For a while, this made Spain enormously wealthy and enabled it to finance armies and conquests on a scale not seen since at least the Roman Empire. It turned Spain into a global power and led to enormous changes in the economies of South America.
Also worth noting is the impact that the silver mines of Laurion had on Athens. These enabled the building of the Athenian navy which played a key role in defeating the second Persian invasion of Greece in 480 BC, and later helped Athens build her empire.
SPAIN AND SOUTH AMERICA
The amount of silver brought by Spain to Europe was enormous (see stats here), more than Europe had ever seen before. The wealth from South America meant that
In the beginning of the sixteenth century Spain stood, in relation to the
other nations of Europe, economically higher than she had ever stood
before, or has ever stood since.
Further, these conquests and often ruthless exploitations
laid the foundations of a truly global trade by opening up the great
trans-oceanic trade routes and the exploration of unknown territories
and oceans for the western knowledge.
The exploitation of the New World also completely changed the economies of the Americas: the settlement of thousands of Europeans engaged in economic activities transformed the continent.
There were also some huge downsides to this for many people, most obviously for those whose gold was taken and for those forced to extract (under often appalling conditions) the silver from the mines. Also, the Price Revolution (believed by most academics to have been primarily a result of the huge amounts of silver pouring into Europe) caused massive inflation in much of Europe (in Spain at least, this hit the poor hardest). It also bankrupted the Spanish monarchy due to successive kings' failure to exercise proper control over the flow and use of silver and gold.
On the other hand the Price Revolution (acknowledgement: Pieter Geerkens for his comment below) was a major economic stimulus:
This important period of economic growth in Europe fostered a new system of economics that would change the world. This new system relied on supply and demand and fluctuating prices. These new ideals and practice are what evolved into our modern system of economics called capitalism....
...The impacts of trade, the change in price, struggle to gain land and
power, and especially a new system of economics brought forth a new
era and forever changed the way the world is run.
ATHENS IN THE CLASSICAL PERIOD
The importance of the the mines of Laurion to Athens is well stated by Robin Osborne in Classical Greece 500 - 323 BC. On the importance of this in resisting the Persian invasion:
In the late 480s, a major silver strike resulted, we are told, in a
windfall gain for the treasury of one hundred talents...the Athenians
used the money to build one hundred triremes, which were soon to be
instrumental in defeating the Persians at Salamis and establishing
Athens as the leading naval power in the Aegean
This naval power,
underpinned the acquisition of the empire, which in turn funded,
through tribute and other revenues, the costly Athenian brand of
democracy...without the resources of empire, the Athenians could not
have funded pay for public office (even the poor could take part) and
an all-powerful fleet (one talent in rowers’ wages alone to keep just
one trireme at sea for one month) and supported public works (the
Parthenon, not including the cult statue, cost about 470 talents) and
built up a cash reserve of almost 10,000 talents on the Acropolis
The silver was used to make coins
The silver extracted from the mines was formed into the Athenian
Tetrhadrachmon coin, which became the dominant commercial currency of
the eastern Mediterranean during the classical era. These coins, along
with the tribute paid by their allies in the Delian league, bestowing
even more wealth upon Athenian citizens who used it to maintain their
empire and to finance grand cultural projects.
Production declined during the Peloponnesian War (431 - 404 BC) and Sparta's capture of the fort at Dekelia in 413 BC made it difficult for Athens to access the mines.
Other sources / further reading:
Douglas Fisher, 'The Price Revolution: A Monetary Interpretation'. In The Journal of Economic History Vol. 49, No. 4 (Dec., 1989), pp. 883-902
Bernard Moses, 'The Economic Condition of Spain in the Sixteenth Century'. In Journal of Political Economy Vol. 1, No. 4 (Sep., 1893)
New World Encyclopedia, 'Spanish Empire'