War was by no means uncommon in the Middle Ages, whether among Christians or otherwise. It's difficult to speak about it in general, because the Middle Ages tends to span an era of almost a thousand years (around AD 500-1500). There were different conditions and cultures in 1300s Germany and 800s Britain and 1100s Italy and 600s Spain.

However, to play to one of the more commonly known periods of the Middle Ages, let's look at the Hundred Years' War between the Kingdoms of England and France. It lasted from 1337 to 1453. This war goes back three centuries, to when Duke William of Normandy became King of England in 1066. Normandy was a "vassal" state of France, so that William had to pay homage to the King of France as his lord and master. Later on, through marriage and inheritance, the Kings of England gained many other lands within France. However, importantly, despite being King of England, they had a dual role as a vassal to the King of France. So, even though as Kings the two were equal, as Dukes of Normandy and of Aquitaine one had to pay tribute to the other (whether in gold, men, support for a war, etc.) The English kings hated this. A LOT. It both rankled their pride and made legal problems and dealing with the Church a lot more difficult.

So, comes a time in 1328 when Charles IV of France dies with no male heirs. Well, look what we have here: his closest male relative, his sister's son, is Edward III. This is why you can trace a lot of medieval war to the inheritance laws of the time, in particular the Salic Law. Under Salic Law, territories passed to the closest male relative. However, the French nobles, whose power would be reduced by uniting the kingdoms, argued that if Edward's mother couldn't inherit the throne, then Edward couldn't inherit it either; this meant that the crown went to Charles IV's first cousin, who became Philip VI.

Edward wasn't prepared to argue over this, so he came to pay homage to Philip VI as the Duke of Aquitaine. To pay homage, vassals were supposed to come unarmed and with their heads uncovered; Edward III came with crown and sword, a direct insult to Philip VI.

The French court decided that, for this reason and others, Aquitaine would be seized and Edward III stripped of his titles. Edward, in response, decided to push his claim for the French throne.

Here we see one of the main reasons for Middle Ages warfare: law and inheritance. A lot of the struggles were legal disputes taken to a whole other level. There was no neutral arbiter; the Church could step in, but the Church always had an agenda as well, so people might pay attention to them - or not. In 1340, the Church even ruled that men could not inherit through their mothers (in short, ruled against Edward) but that definitely didn't stop things. This got even more complicated when different bodies of law (for instance, Norman Law vs. Angevin Law in the succession of Richard I of England in 1199-1200) came into play. Each law said a different party would inherit the throne.

Note that this is only one example. There were plenty of reasons for war, but a lot of Middle Ages warfare, and indeed European warfare all the way to the 1700s (see: War of the Spanish Succession, for instance) relied on legal issues and inheritance laws. Basically, someone died, who does their stuff belong to? Let's fight it out.

Other popular reasons for war: Heresy (Albigensian Crusade, Hussite Wars). If anyone wants to talk about that I think I'm about talked out.

Sources: Crecy 1346: Triumph of the Longbow by David Nicolle. Oxford: Osprey Publishing, 2000

The Hundred Years War 1337-1453 by Anne Curry. Oxford: Osprey Publishing, 2002

Edit: Formatting.