There have been numerous events in history where the validity of the event has been questioned because of a lack of formal declaration. For instance, in the Vietnam War, and in the Korean War. The Korean War was actually referred to not as a war but as a "United Nations 'Peace Action'" even though more than two million people were killed as a direct result of the conflict, and no resolution was ever made between the United States and North Korea.
An example illustrating whether a war has to include actual physical violence (a battle), is the "War of Bavarian Succession", nicknamed the "Kartoffelnkrieg" or "Potato War". A declaration for war was made and fully armed militants from wither side met face to face, but no shots were ever fired, and no deaths resulted before a peaceful resolution was found.
The question on whether war must be between two (or more) formally declared nations or States has been the subject of disagreement. Some have brought up the question on whether National Governmental Organizations (NGOs) have the right to wage war. While NGOs are not identified by the international community as States, in the sense that they do not occupy a territory, they do display many other characteristics of a State. The main point is that war has an ever evolving face. New variables are constantly tied in, and old ones are constantly disagreed upon, as one man wrote, "...most people