The Postage Stamp War
Some wars have been started by pretty trivial things (like when Saddam didn't like Kuwait's attitude back in 1990) but it's hard to come up with a more petty reason than a postage stamp. Yet, that was one of the factors leading to the Chaco War (1932–1935).
Both Paraguay and Bolivia claimed an uninhabited desert region called the Gran Chaco. Bolivia, landlocked after war with Chile, wanted the territory in order to give it river access to the Atlantic. Paraguay, having lost most of its territory to its neighbors during the War of the Triple Alliance, needed the Gran Chaco just to stay on the map. Both sides believed there were rich oil reserves in region as well.
The dispute heated up considerably when Bolivia issued a stamp featuring a map of Bolivia... a map that included the Gran Chaco, now marked as Chaco Boliviano. Paraguay didn't take this sitting down, and soon issued even bigger stamps than Bolivia, with an even bigger map of the Gran Chaco, but this time marked as Chaco Paraguayo.
Bolivia had no intention of allowing Paraguay of getting away with this postal raid, and so moved forces into into the Gran Chaco. And Paraguay, for its part, couldn't wait to get it's licks in as well and did the same. Soon, Philatelic Warfare gave way to the real thing and in 1932 both sides were shooting at each other in earnest.
The Chaco War saw the use of armor and aircraft on both sides. British, American, French, and Italian arms makers took the opportunity to export some of their newest weapons to the combatants. German and Russian veterans of the First World War were on the staffs of both sides, advising the armies of Bolivia and Paraguay
In the end the Paraguayans won. It was just as well... the Paraguayans got the Gran Chaco but it turned out that the oil everyone thought was there didn't exist.