The 1796 Quarter Eagle with No Stars on the obverse is one of the most historic and important U.S. gold coins. The mintage is a mere 963 pieces, which is exceedingly small by any standard. Estimates of the number of surviving examples has ranged all over the place. David Akers claimed 30 to 40, refuting earlier claims of 15 to 20 known. The cataloger at Heritage estimated 80 to 100 in their January 2007 sale. PCGS experts estimate a surviving population of 100 to 125 pieces. To put a finer spin on things, we have images of 28 different examples, all in AU or better. Eleven of those examples are Mint State 60 or better. At the top of the condition census is the incredible PCGS MS65 (finest by two full points) that sold for $1,725,000 in January 2008.
It is very difficult to locate a "perfect" 1796 No Stars Quarter Eagle. Many show lintmarks of various sizes. Some show adjustment marks, usually in the center of the obverse. The Bass:261 coin (now in an NGC MS60 holder) shows three different, mint-caused defects: a diagonal fissure running from the turban to Liberty's temple; vertical adjustment marks on the obverse; and a heavy lintmark on the right side of the reverse (yet, it is still a nice, six-figure coin). Though there are numerically finer examples, my personal favorite is Bob Simpson's PCGS MS62+ -- it is well-struck, has great color, and is free of any distracting problems.