Given your date range, the first event that comes to mind is the Thirty Years War (1618 - 1648). The relative devastation of that conflict is staggering.

Given that date range and location of Europe, the first thing I thought of was the Ottoman Empire siege(s) of Vienna.

I grew up in Saudi Arabia but we never learned about the Muslim/Turkish invasion of Europe. In school, we mostly focused on the Reformation during that time period.

I didn't learn about the 1529 and 1683 Siege of Vienna until I was eating at a restaurant in Vienna back in 2003 and our restaurant had cannonball holes in the wall and I'm pretty sure there was even a cannonball stuck in the wall.

So there's some violence in Europe during the specified time period.

War was endemic in Europe, pretty much from the beginning of recorded history until the end of the Napoleonic Wars in 1814. Even the Pax Romana only existed inside the Roman empire, not outside. The idea that peace was the normal condition is a relatively new one, historically speaking. See Sir Michael Howard, The Invention of Peace.

Probably most relevant to the early European involvement in the New World was the Reconquista - the Christian reconquest of the Iberian peninsula from the Moors. This ended in 1492 - the very year Columbus discovered the New World. So conquering heathen for God and monarch was definitely nothing new to the Spaniards.

Also during this same time period, there was the Hundred Years War between France and England, followed by the Wars of the Roses in England.

In my opinion, the Spanish are really the only ones who can be said to have really conquered portions of the New World, at least in the military sense. By the time the French and English start claiming chunks of territory and setting up colonies, the native population has been devastated by the inadvertent introduction of European disease. I've seen some estimates that the pre-Columbian population of the New World was reduced by up to 90% in the roughly 125 years between Columbus and the Pilgrims' arrival. The French, Dutch, and English were thus moving into areas that had a lot of empty space. (Many of the 'open fields' found in New England, for example, were actually cleared fields, but the natives who had cleared them had either died or left the area as the population thinned.)

The Spanish conquistadors of the early 16th century were thus the only Europeans encountering native societies at their height. (Neither the English nor the French, for example, sent expeditions to Cahokia to subdue the mound-builders.)

Also keep in mind that Christian Europe was in conflict, sometimes outright war, sometimes not, with the Muslim Ottoman Empire during that entire time period. Constantinople finally fell in 1453, the first Siege of Vienna was in 1529, and the second in 1683. This was much more of a concern for the Holy Roman/Hapsburg Empire, the Italian city states (Venice, Genoa, Florence), and Mediterranian kingdoms than England and France. But it was part of the constant warfare of the period.