The Flag of the United States Navy, as defined in s:Executive Order 10812 of April 24, 1959.  The design is described there as:
The flag for the United States Navy is 4 feet 4 inches hoist by 5 feet 6 inches fly, of dark blue material, with yellow fringe, 2½ inches wide.  In the center of the flag is a device 3 feet and 1 inch overall consisting of the inner pictorial portion of the seal of the Department of the Navy (with the exception that a continuation of the sea has been substituted for the land area), in its proper colors within a circular yellow rope edging, all 2 feet 6 inches in diameter above a yellow scroll inscribed "UNITED STATES NAVY" in dark blue letters.
The U.S. Navy flag is used for display purposes at ceremonies, parades, and other public functions where the U.S. Navy has an official presence, usually being carried by an honor guard on ceremonial occasions.  It is not used for outdoor, fixed (permanent) purposes, and is not flown on Navy ships. Versions without fringe and different dimensions seem to be common, though it appears they are not technically the official U.S. Navy flag, as the executive order has not been amended.
Prior to 1959, the Navy Infantry Battalion flag was used to represent the U.S. Navy.

For more information, see the Navy's flag history page, SeaFlags, Flags of the World, U.S. Navy document NTP 13(B) [1], section 1710, and Navy regulation OPNAVINST 10520.1 (which replaced a similar SECNAVINST 10520.2D regulation from 1974).
Seal portion and rope edging taken from File:US-DeptOfNavy-Seal.svg, a U.S. Navy work; the rest self-drawn following images like File:Navy flag.gif.
United States Department of the Navy