Ron Guth: The 1884 Three-Cent Nickel has the second lowest circulation-strike mintage of any date in the series (second only to the 1885). Even better, it has the fewest number of Mint State examples of any date in the PCGS Population Report...by far.
PCGS has certified only 39 1884 Three-Cent Nickels in all grades, compared to 85 for the 1885. MS-64 and MS-65 are the most populous Mint State grades (though only 2 of each can hardly be considered momentous). The finest example certified by PCGS is a single PCGS MS67. Circulated examples can be found in a wide range of grades between VF-20 and AU-58.
Beware of Proofs masquerading as Mint State examples...sometimes they are hard to tell apart, and the Proofs are worth much less than the Mint State versions.