-Hidden (Shinobi) Wars in general: reasons, consequences and what might have been:
1: While not all historians agree on the naming, the general consensus is that each of the three major conflicts in the last century were the first wars where modern ninja played significant roles. Ergo, they were named the Shinobi Wars. "Hidden Wars" is also a popular term for the conflicts due to the ninja involvement and the covert actions behind the large scale battles.
The First Ninja War (60 years Pre-Kyuubi) was the result of the current Daimyo of Wind Country being possessed by the demon later known as Shukaku, who led Wind on a campaign of conquest. Earth country's fragile confederation of states was broken by the onslaught, but an alliance between the Fire Republic, the Kingdom of Snow and the Water Confederacy was able to use Fire Country's superior industrial and naval might to hold back Wind's assault. Combined with the rebellion of the Sand Village against the oppression of the Daimyo, and the strength of Leaf and Mist Village, the demon-container was defeated. Wind Country's subsequent government, the Wind Kingdom, became closely allied with Fire, the new superpower, while the economic strain of the war made Water Confederacy weak and its ninja village strong. Earth Country was sent into a series of civil wars (again), which led it to ultimately ally itself with the Lightning Union, which had watched the war. After, they began their own preparations.
This was also the first war where Leaf and Fire fought together against a single foe since the village's founding, and catapulted the First and Second Hokage into legendary status around the continent. It also resulted in the Kingdom of Snow's decline as a military power, instead converting their economy into a consumer-based one to provide goods bought up by the growing middle class in Fire and Wind as the latter's economy recovered.
2: The Second Ninja War (32 years Pre-Kyuubi) was the result of the Earth/Lightning Alliance making a bid to become the new superpower of the continent against the Fire Republic. To do this, they provided massive support to Rain Country, the current leadership being deposed in a coup supported by the current Rain Village leader, Hanzo. Rain Country would annex nearby nations and draw the Fire Republic into battle, which was currently led by the Nanashi Party. The Nanashi party was anti-war and anti-military, and Earth and Lightning felt that by forcing the Republic into a prolonged conflict in Rain would weaken them enough for an eventual full scale war to grant them victory.
Rain Country launched invasions of River, Bird, Rice and Wave countries. The Fire/Wind Alliance went to war to liberate these nations, the conflict becoming an all-out continent war with the advent of the airship and the direct entrance of Earth and Lightning into the conflict when the majority of the Republic's forces were deployed. Water Country tried to support Fire and Wind, but a disastrous loss at the Battle of Jasmine Bay in Wave Country to the Lightning Fleet resulted in the Water Daimyo becoming weak enough for the Seven Swordsmen of the Mists to attempt a coup. Water Country was, subsequently, out of the war. Wind Country bore significant losses in the conflict, and the Northern Republic Navy was initially crippled by a joint Lightning/Earth fleet assault on their primary naval base.
Despite all this, the tide was turned with two key actions: The defeat of the Rain armies by the Sannin of Leaf, and the destruction of the Earth/Lightning Fleet at the Battle of Fang Island by the Fire Republic Navy. The war stretched on for another two years and saw Fire Country's Army breaching Lightning Country's borders for the first time and the Fire Navy and Air forces gaining control of the seas and air. After the Battle of Kyon-Ko, where the majority of the Earth army was destroyed and the Lightning army halved, the Alliance quickly came to the negotiation table. The Earth and Water Confederacies both fell into civil war again, this time coming out with their ninja villages being the main powers in their governments. Lightning Country was humiliated, and focused more on information gathering and diplomatic warfare rather than overt military buildup. And Fire Country obtained a virtual monopoly over the skies and seas with their airships and Navy.
Of course, if it were not for the Sannin, the war may have turned out quite differently. Their daring actions at the beginning of the conflict kept the Fire Republic from becoming embroiled in a single war to wear them down which would have allowed Earth and Lightning to swoop in. It also led to the Nanashi Party losing significant face in the eyes of the public, given that they allowed this buildup to occur.
One final note was that is was the first conflict with airships in a military role, and the last recorded battle between a Cult of Jashin Warrior and two Yamanaka Witches who had accompanied the Sannin Armies.
3: The Third Ninja War (5 years Pre-Kyuubi) was sparked with the rebellion of Grass Country against Earth, declaring it's independence from Earth's corrupt, unstable government and forming a republic. Lightning support its longtime ally Earth as it tried to crush the rebellion, more out of obligation than anything else and perhaps a chance to get its hands on some of Leaf Village's bloodlines. It had the least conventional military involvement of all the Hidden Wars, though Republic airships did offer humanitarian aid and occasional fire support. The primary reason was due to the testing of a new doctrine, coined the SEED Doctrine. The premise was to let Leaf Village establish ninja villages in friendly nations and the Republic to provide support to said villages in order to allow them to defend themselves, rather than forcing the Army itself to intervene.
The strategy worked well. Grass Country became free and prosperous, and one of Leaf Village's rising stars, Namikaze Minato, became feared in Earth and Lightning Countries as the Yellow Flash-A warrior without peer.
Some historians have argued that this war was not large enough to constitute a true Hidden War, comparing it to a smaller conflict known as the Bird Country War that Fire intervened in three years prior. However, given the significance of the Yellow Flash's contributions, it was decided that this conflict would be considered a true Hidden War.
It also marked the first official appearance of Akatsuki, and the last conflict the ANBU organization ROOT was officially part of before being disbanded by the Third Hokage.