Answer: It would be difficult to name a single favorite. I, like others, agree that Augustus Saint-Gaudens’ MCMVII (1907) double eagle is either at the top of the list or certainly in the front rank. My appreciation of this coin has deepened in later years after I wrote about Saint-Gaudens in particular and gold coins in general, did a book for Whitman on double eagles, and visited the Saint-Gaudens National Historic Site. Probably this would be #1 if you combined beauty plus history plus personal interest.
I have many other favorites. The 1796 British Settlement in Kentucky token by Myddelton is beautiful. In 1875, Sylvester S. Crosby said it was the most attractive design related to the early American series. The Libertas Americana medal made in France to the order of Benjamin Franklin is another gorgeous piece — not a coin but certainly numismatic.
Among later issues I like the Flowing Hair silver coins of 1794 and 1795 — perhaps not the epitome of art, but certainly attractive with their hand-made dies and features that typify early American numismatics. The Indian Head cent of 1859 to 1909 is another favorite — very appealing. A curious thing about copper coins, unlike gold, is that a well-worn Indian cent can be an object of beauty. Ditto for any early copper coin. On the other hand, if someone had a Liberty Head double eagle in VG or Fine grade it would not be considered collectible or desirable. Interesting to contemplate!
The Walking Liberty half dollar from 1916 to 1947 is beautiful and another favorite. Ditto for the 1916-1930 Standing Liberty quarter, particularly the Type I variety of 1916 and early 1917. Among recent coins I like the 2000 New Hampshire Statehood quarter, not because it is overwhelmingly beautiful — in fact, it has been criticized although not by me — but because I was at the launch ceremony, covered it for Coin World, and later featured the event as a chapter in my More Adventures with Rare Coins book. More recently I attended the launch ceremony for the 2013 New Hampshire National Parks quarter. Actually New Hampshire does not have a national park, so the White Mountain National Forest was honored with the coin, designed by Phebe Hemphill, featuring the outline of Mount Chocorua — which is not very far from where I live. Actually, in a broad sense I like most of the designs, and even a 1793 Chain AMERI. cent, widely criticized in the press when it was first issued, to me is an object of rare beauty!