Looks like we're almost tied with Vietnam and working on WWII
Conflict Cost in $ Billions Per Capita
Current 1990s (in $1990)
The Revolution (1775-1783) .10 1.2 $ 342.86
War of 1812 (1812-1815) .09 0.7 92.11
Mexican War (1846-1848) .07 1.1 52.13
Civil War (1861-1865): Union 3.20 27.3 1,041.98
: Confederate 2.00 17.1 2,111.11
: Combined 5.20 44.4 1,294.46
Spanish American War (1898) .40 6.3 84.45
World War I (1917-1918) 26.00 196.5 1,911.47
World War II (1941-1945) 288.00 2,091.3 15,655.17
Korea (1950-1953) 54.00 263.9 1,739.62
Vietnam (1964-1972) 111.00 346.7 1,692.04
Gulf War (1990-1991) 61.00 61.1 235.00
" The table compares the cost of America's principal wars since 1775 on the basis of then current and 1990s dollars. Current dollars are the actual numbers spent at the time. Thus, a 1775-1783 dollar had the equivalent purchasing power of $10.75 in 1990s terms. Actually this conversion is only a very rough guide, but at least gives some idea of the relative costs of the ten wars on an adjusted basis. However, it is not possible to take into account drastic changes in social structure (most Americans were farmers in 1775, and didn't use much money), and the increasing affluence of American society over the two centuries covered by the table."
http://www.cwc.lsu.edu/cwc/other/stats/warcost.htm