The 1901 Half Dollar is common in just about every grade in which it is found. The exception, of course, is in the grades of MS66 and MS67 where, like most Barber Halves, this date is very scarce. None are known above MS67. The 1901 is decidedly less common in superb condition than the 1900 and 1902, but it is not nearly as rare as the 1903 -- it more closely mirrors the 1904 and 1905.
The superb Thaine coin (mentioned below by Akers) is currently in a PCGS MS67 holder. It is a remarkable coin, with intense luster and gorgeous color. It's companion is the equally appealing PCGS MS67, formerly of the Shireman Collection.