The 1804 Draped Bust Quarter Eagle (Buy on eBay) with 13 stars on the reverse is an extremely rare variety created through an unusual set of circumstances.
In the early days of the Mint, dies were often reused across multiple years as a cost saving measure. Additionally, since the dime and quarter eagle were approximately the same size, the same reverse dies were often used across both denominations. One particular die was used to strike 1802 quarter eagles, 1804 dimes, and a small number of 1804 quarter eagles. These coins carried 13 stars on the reverse, while the vast majority of other 1804 quarter eagles carried 14 stars.
Although the exact mintage of the 1804 Quarter Eagle 13 Star Reverse is unknown, fewer than a dozen pieces are known to exist. The finest known example graded AU-58 by PCGS sold for $322,000 in 2009, although lower graded pieces have subsequently sold for higher prices.