Americans say Marines are most prestigious.
Gallup first asked Americans about the importance of the military branches in the 1940s, and began using the current question wording in 2001. Regardless of exact question format, at all points prior to 2004, Americans -- by very substantial margins -- have named the Air Force as the most important branch of the military.
A major shift occurred between 2002 and 2004, concomitant with the beginning of the Iraq war in which the primary focus of news coverage was on the actions of U.S. ground forces. The percentage of Americans naming the Air Force as most important military branch declined in 2004, while Americans placed more importance on the Army and Marines.
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My Comment: Those serving in the Coast Guard are probably going to be disappointed with this poll result.