There are a couple things to consider about the period in question.

I think your question might be a bit biased towards Anglophone history. There is nothing wrong with this, of course! I merely mean to say that the framing of your question seems to focus overly much on Anglophone countries; for instance, 1066 was not really a huge year in some parts of Europe, but obviously it was a big deal in England and Northern France. Again, the Hundred Years War was essentially just between England and France. Obviously, there were conflicts happening all over Europe in this period. I just mean to say that Germany or Italy, for example, certainly weren't experiencing some golden age of peace.

Secondly, the practical realities of medieval warfare, defined by both technology and the prevailing strategic mindsets of the time, dramatically favored the defender in almost any conflict. In this period, wars were more like a series of protracted sieges that could take years, with pitched battles being relatively rare in comparison to earlier and later periods. So, in a way, wars were less 'dramatic' in this period -- and certainly much slower.

Many nobles were also obliged to allow the bulk of their soldiers to return home for harvesting and planting, so active 'campaigning' was limited to specific seasons (mostly the summer. Farming work needs to be done in spring and fall, and you can't use the roads in winter, so your medieval strategist is pretty limited in when he can even have an army). This is another reason why pitched battles were relatively rare.

Rather than having a few high-profile wars like WWI and WWII, where huge alliances were involved, many medieval wars were much more localized, they stopped and started often, and were kind of endemic. It was hard to tell the difference between, say, bandits, and poor knights. Especially when the richer knights basically behaved like bandits as well...

If you are interested in specific wars in the historical period, there are a number of interesting conflicts. For instance, after the First Crusade, England experienced a period of civil war known as "the Anarchy." There were a huge number of conflicts between the Holy Roman Empire and the Papacy (with various other factions involved) in Northern Italy. During the High Middle Ages the Christian kingdoms of the Iberian peninsula fought the Reconquista, mostly recapturing the peninsula from the Moors by 1248 (completed in 1492). During this time is when countries like Portugal, Castile, and Aragon were established.

There were also localized Crusades, ie, crusades against heretics in Europe rather than against external powers (such as the 'classic' crusades in the middle east or the northern crusades against pagans in Eastern Europe and Russia), like the Albigensian Crusade. These are less like wars and more like an inquisition, but they are still interesting to study. Especially interesting to me in these cases is the resistance of people who remained heretics in secrecy, eventually forming the seeds of the Protestant Reformation.

It's not really Europe, but the Byzantine Empire was constantly involved in fighting the Seljuks in Anatolia in this period (obviously, since you have ended the period with 1453 :P and arguably this is part of the Crusades). I would argue, though, that to consider Europe in isolation in this period is wrong, as we are really talking about a relatively shared economic/political culture around the whole post-Roman mediterranean. What happened in the Muslim Near East and North Africa absolutely effected what was going on in Europe and vice-versa.

The Mongol Invasions did not effect Western Europe so much but they were absolutely a defining moment in Russian/eastern European history (and the western kings were aware of what was going on; for instance, the King of France wrote the Khan a letter when the Mongols invaded Hungary). The effect on modern Russian culture cannot be understated; many Russian words relating to statecraft, bureaucracy, and torture descend directly from Mongolian as a result of the Mongol Yoke.

The picture I am trying to paint here is that it was a very violent period and pretty much everywhere you look you can find some kind of conflict. Whether for religious, economic, or political reasons, there were all kinds of battles going on in this period, but they do not necessarily line up with our modern conception of how a war is prosecuted, due to the technology and culture of the time.