Four significant battles in history:
Salamis Arguably the first great naval battle. There were fleets before, 'tis true, but part of the reason for its significance is that the Athenians (and the Greeks in general) relied heavily on maritime economy for their livelihood, so the outcome of the battle was more important than if it had been a land fight for the city itself (which, incidentally, had been evacuated and abandoned). This not only ended further Persian expansion in the Aegean and set the course of Athenian strategy until the end of the Peloponnesian war, but established the very idea of a "naval power".
Tours Charles Martel shut down expansion of Islamic/Moorish empire into Europe by defeating a force superior in both numbers and theoretical power (though it seems that Frankish infantry had better arms and armor than their opponents). The Moors would have lost a major battle sooner or later, but if they first established a foothold over
the Pyrenees it would not have been so easy to push them back out of Europe (as it is it took about six centuries after the battle to finally drive them out).
Tenochtitlan A siege, rather than a stand-up battle, but it guaranteed Spanish control of Mexico and most of the New World, setting the stage for rivalry with the Portuguese, Dutch, and English for the next few centuries. It also was the beginning of a new process of colonialism; previously colonies had been confined to strategically important ports and costal areas (such as along the African coasts, Goa, Malacca, etc), but Cortez and Velazquez were the first to conceive of seizing and exploiting the interior land themselves, instead of simply trading for its products.
Austerlitz Basically the last great battle of tactical maneuvers. It solidified Napoleon's reputation as a brilliant commander and made him public enemy number one for all of Europe. It also convinced the Spanish and Russians that beating on a level playing field was virtually impossible, influencing their decisions to rely on guerilla tactics and scorched earth instead. This, in turn, continues to influence military and foreign policy today. Since then, strategic advantage (in the form of equipment, material, intelligence, and planning) have become the decisive factors in warfare. I remain convinced that the decisive battle of the American civil war was in fact Vicksburg, and not Gettysburg, for the simple reason that it brought someone who understood the new reality of war to prominence in the form of General Grant.