https://en.wikipedia.org/wiki/Declaration_of_war_by_the_Unit...
For example, the U.S. was officially at war with Japan from 7-8 December 1941, for a few hours with Germany and Italy on 11 December following their declaration of war against the U.S., and from 13 December 1941 to 6 June 1942 against Bulgaria.
https://en.wikipedia.org/wiki/United_States_declaration_of_w...
http://en.wikipedia.org/wiki/United_States_declaration_of_wa...
http://en.wikipedia.org/wiki/United_States_declaration_of_wa...
The American Civil War was considered an insurrection by the victor (Lincoln), thus that's what it'll go down as in the history books.
Certainly the casualty count on both sides makes Vietnam count as a 'war'. And yet, Congress actually declaring a state of war would have given Presidents Kennedy or Johnson vast and sweeping powers, which was something that Congress would be loath to do when the President was already able to kill Commies sufficiently well by simply letting him engage in 'armed conflict' without the state of 'war'.