This is the popular early federal coinage designed by Benjamin Franklin and so named for the word FUGIO ('I fly'). The copper coin was to circulate with the value of one cent, but no denomination is stated on the coin. It is curious that modern American politics has changed dramatically since 1787. 'Mind Your Own Business' is exactly opposite today's 'Political Correctness,' and 'We Are One' is exactly opposite today's 'Strength Through Diversity.'
Evaluating these coins is a bit beyond this simple CoinQuest forum. There are several different varieties of the Fugio copper, and values change with variety. For a good run-down on varieties with value estimates, see this page at CoinAuctionHelp. Further, the coin has been re-struck and reproduced several times, with plenty of un-marked fakes around. You can view a thorough treatment of fugio cents at the Department of Special Collections, University of Notre Dame, Notre Dame, Indiana, including a description of restrikes. Authentication by PCGS, NGC, ICG, or ANACS is strongly recommended for any fugio copper.
With the qualifiers of the previous paragraph, we give below some approximate average data:
FUGIO CENT: AVERAGE VALUES FOR THE COMMON VARIETIES
worn: $200 US dollars approximate catalog value
average circulated: $1000
well preserved: $3000
FUGIO CENT: UNITED ABOVE, STATES BELOW VARIETY
worn: $600 US dollars approximate catalog value
average circulated: $7000
well preserved: $10000
FUGIO CENT: CLUB RAYS WITH CONCAVE ENDS VARIETY
worn: $1000 US dollars approximate catalog value
average circulated: $15000
well preserved: $28000
The values above are catalog values. Read our Terminology page to convert these catalog values to actual buy and sell values.
For a little more insight into value, consider the four coins shown in the graphic below, labeled (A), (B), (C), and (D).