(I was going to post this, but decided to flesh out some of the details I'd seen in an earlier post.) My offer for an overlooked war: the Axumite invasion of Arabia.
Axum (alternate spelling- Aksum) was a city-state that controlled roughly present-day Ethiopia. The kingdom converted to Christianity (coptic) and allied with the Byzantine Empire against the Persians. As part of the war, the Axumites invaded southern Arabia. They conquered rich southern Arabia (Yemen) and began to push into central Arabia (Mecca/Medina), bringing a large army with elephants. They ended up pulling back (whether because dificulties campaigning so far from home or new ruler back home, I don't remember). They retained control of Yemen and harassed Persian hold of eastern Arabia (Oman), forcing the Sassanids to stretch their resources.
It got more interesting when Muhammed came along. Initially, he didn't have alot of support in his home town (Mecca) and so he sent his relatives and followers away. He ended up at the Axumite king's court, requesting assitance. Nothing came of it, but just goes to show you the influence the Axumite kingdom had on the region.
(Commenting on some of the earlier stuff...) People seen to forget that the United States was one of the states that invaded Russia in support of the White Russians. I think (though I admit, I dont know) the reason is that every other state (Poland, Britian, France) invaded the western side, but the United States invaded Siberia.
Also, I think any of the wars at the beginning of the 20th century that facilitated the breakup of the Ottoman Empire would be something to focus on. Specifically, the exploits of the Yoguslav state, since it inflamed Pan-slavic nationalism, encouraging Russia's hostility with the Austro-Hungarian Empire, and precipitating World War I.