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Louis Eliasberg, the Baltimore financier who died in 1976, famously collected U.S. coins, amassing examples of each denomination, type, year and mint mark ever produced. His extraordinary holdings included an exceptionally rare 1933 Double Eagle $20 gold coin. No coin collector since has accomplished his comprehensive feat—and probably no one ever will—but all recognize the single-minded passion that led Eliasberg to pursue so Herculean a goal.

The vast majority of coin collectors in the United States focus on U.S. coins, says Rodney Gillis, an educator at the American Numismatic Association, and most of them build sets comprising either one example of every type or of every year and mint mark for a single type. A great thing about coin collecting is that you “can do something very nice at lots of different price points,” says Gillis. “For $100 or $150, you can have a complete set of Franklin half-dollars,” a classic design, made from 1948 through 1963, that features the bust of Benjamin Franklin on the obverse and the Liberty Bell on the reverse.

According to Robert Korver, a director emeritus of Heritage Auction Galleries, which sells coins and other collectibles at its Dallas headquarters and other locations, as well as online, the numismatic market today is the “hottest it’s been in two decades.” He attributes the intense interest not just to high metal prices but also to the advances in Internet auction sites, where collectors can easily view images of coins before bidding. (In fact he credits the superhigh resolution of the pictures on Heritage’s Web site with making it the leading numismatic auctioneer.) As Korver sees it, the ease of buying online drives up demand, which in turn drives up prices. Harvey Stack, of the New York-based dealer Stack’s, cites too the extraordinary popularity of the U.S. Mint’s issues of commemorative coins, such as the series of U.S. state quarters, which was first released in 1999 and ends this year.

Rare coins in good condition can command truly stratospheric prices. At a July auction that Stack’s held in Baltimore, a number of early American coins fetched six-figure sums. And more than 20 U.S. coins are known to have sold for more than $1 million. Last year the California dealer Ronald Gillio arranged the private sale of a 1913 Liberty Head nickel, an alumnus of the Eliasberg collection, for $5 million. And in a joint sale in 2002, Stack’s and Sotheby’s sold a 1933 Double Eagle for $7.6 million, the most ever paid for a coin.

Designed by Augustus Saint-Gaudens, the celebrated 19th-century American sculptor, with the figure of Liberty on the obverse and a flying eagle on the reverse, the gold $20 coin was produced from 1907 through 1933. Most Double Eagles in excellent condition can be bought for less than $1,000. What makes the 1933 issue so valuable is that shortly after it was minted, the United States went off the gold standard, and the circulation of coins in this metal was outlawed, so the issue was never released. Most of the 445,000 coins were destroyed, but at least 10 are believed to have been stolen and sold by George McCann, the Mint’s chief cashier. Over the years, agents from the U.S. Secret Service recovered them. The one sold in 2002 was the last, put on the block in settlement of a suit against its owner, the British dealer, Stephen Fenton, filed by the federal government, which split the proceeds with him.

Another numismatic niche is ancient coins, typically either Roman or Greek. “They say that Roman collectors are interested in history, and Greek collectors are interested in art,” says the New York coin connoisseur Jeff Benjamin. “The Romans didn’t have newspapers, so when the emperor wanted to get a message across, he did so by putting it on the back of a coin.” The announcements might be mundane, like the notice of a tax reduction, or they might be celebratory, like the proclamation of a military conquest. Benjamin specializes in post-Republican Roman sestertii, bronze coins about the size of a half-dollar that were issued from the middle of the first century B.C. through the third century A.D. Prices range from $25 for worn specimens to more than $100,000 for ones in pristine condition, especially those produced for Nero, which are noted for their fine engraving.