Above all, the United States Mint’s responsibility is to issue coins for circulation thus producing money needed for day-to-day commerce. A secondary (but often lucrative) ancillary activity has been the production of proof coins for collectors. The US Mint is often incentivized to strike proof coinage, as it typically gets a premium for these special collector editions that far exceeds normal face (or bullion) value.
There have been numerous occasions where certain coins had limited commercial demand—or no demand at all! Nonetheless, to satisfy the needs of collectors (and to pick up a small profit), the US Mint struck a small quantity of proof issues. These instances are few are far between, but they have become some of the scarcest and most celebrated issues in all of numismatics.
One famous proof-only issue that comes to mind is the 1863 Quarter Eagle. When the Civil War broke out, there was a severe shortage of gold bullion. Commensurately, the Philadelphia Mint drastically cut back on striking gold coins of all denominations that year. It decided that no quarter eagles were needed for circulation, but it still struck a small run in proof format. Apparently a small but dedicated group of collectors insisted on buying a proof issue of every denomination that year. As one can imagine the 1863 proof quarter eagle is a major rarity with a mintage of just 30 pieces. One example sold for close to $200,000 at auction in 2012.
An even more extreme example is the proof Trade Dollar of 1885. The Trade Dollar was first introduced in 1873 for use in Asian commerce. The hope was that the coin would be widely accepted and used overseas, but ultimately this never came to fruition. Mintages quickly dwindled and by the late 1870s the coins were only made for ceremonial purposes. Rather than discontinue the denomination altogether, the Mint struck a small number of proofs each year for their loyal collector following. The mintages became absurdly low by the mid-1880s; just ten 1884s were made and then a puny five pieces came off the dies in 1885. One of these 1885 proofs sold for a whopping $3.3 million in 2006!
More recently, the US Mint has created quite a few proof-only issues—but they are nowhere near as scarce as the examples mentioned earlier. Since the 1960s, the Philadelphia and Denver mints have been responsible for making circulation strikes, while the San Francisco facilities have been tasked with making proofs. Therefore most S-mint issues from 1968 onward are technically proof-only coins, but with mintages in the millions, they command rather modest premiums compared to their 19th century counterparts.