[Information from Richard Staley with amendments from Justin T. Broderick]
Admiral (grade created for David Farragut 25 Jul 1866)
Vice Admiral (grade created 21 Dec 1864, Farragut being the
first to hold this rank)
Rear Admiral (created 16 July 1862, the only flag rank that has been
maintained continuously to this day)
Flag Officer (title created 16 Jan 1857, replaced by Commodore on 16 Jun
1862)
Commodore (courtesy title until 16 Jul 1862 when the grade was
formally adopted to replace Flag Officer)
Captain
Commander
Lieut. Commander (grade created 16 Jul 1862)
Lieutenant
Master (originally "sailing master"; after the period was changed to
Lieutenant Junior Grade.)
Ensign (title for a passed Midshipman after 16 Jul 1862)
Passed Midshipman (Midshipman who had passed his examination for
promotion to Lieutenant; called Ensign after 1862 although the term
continued in use.)
Midshipman (grade given undergraduates of the U.S. Naval Academy;
not strictly in the line of the Navy in the latter part of the century).
Master's Mate
Shipped or Rated Master's Mate (usually a warrant officer).
References:
_Todd's American Military Equippage: 1851-1870_
W.B. Cogan, _Dictionary of American Admirals_, US Naval Institute Press,
1989
C.G. Reynolds, _Famous American Admirals_, Van Nostrand Reinhold, 1978
C.O. Paullin, "Naval Administration, 1842-1861", _USNI Proceedings_, vol.
33
J.C. Tily, _The Uniforms of the United States Navy_, Thomas Yoseloff,
1964
http://stason.org/TULARC/history/civil-war-usa/12-What-were-the-naval-ranks-during-the-Civil-War-U-S-Ci.html