Of all the coins made by the San Francisco mint in 1861, the Half Dollar had the highest mintage (the only other coin that came close was the 1861-S $20 gold piece). However, this fact does not make the 1861-S Half Dollar necessarily rare. Compared with other Civil War-era Half Dollars, the 1861-S is not as scarce as the 1864-S or the 1865-S, but nowhere near as common as the 1861 or 1861-O.
Of the roughly three dozen Mint State examples certified by PCGS (as of October 2011), the most frequently-encountered grade is MS-64. Gem 1861-S Half Dollars are very rare; the finest known is a single PCGS MS-66.