Service stripes have been worn on the left sleeves of enlisted Sailors ever since the Navy introduced them near the end of the 19th century. It is a convention followed by all the other Armed Forces of the United States save the Air Force, which eschewed service stripes in favor of its Longevity Service ribbon.
But where the Navy parts ways with the Army, Air Force, and even Marine Corps is in the display of rank insignia—or, to be technically correct, rating badges—on the sleeves of dress uniforms worn by enlisted personnel. The uniforms of those three services feature rank insignia on both the left and right sleeves of their, but the Navy (and Coast Guard) display Sailors’ rate (pay grade indicated by chevrons) and rating (job indicated by an emblem) only on the left sleeve, leaving quite a few folks wondering just how this came to be.
While research doesn’t reveal a definitive answer as to why the Navy opted for the “one-sleeve” system, it does yield some interesting insight as to how the left sleeve was selected for the honor of displaying Sailors’ rates. It turns out that between 1833 and 1885, Petty Officers wore their rating badges based on their job classification: Petty Officers of the Line (Seaman Branch) wore theirs on the right sleeve, all others (except stewards) on the left. In 1885, the Navy changed the system so rating badge placement depended on watch assignments; those on the port side of the ship wore them on the left shoulder, while Sailors assigned to the starboard wore them on the right.
This system lasted until 1913, when the Navy reverted back to rating badge placement by job classification. It wasn’t until 1949 that the regulations were changed so that all enlisted Sailors wore their rating badges on the left sleeve. (Hat tip to the good folks at Bluejacket.com for this information!)