What if, instead of declaring the First Crusade, Pope Urban II had just sent the contingent of mercenary knights that Emperor Alexios Komnenos had actually asked for?
The Eastern Roman ("Byzantine") Empire had a tendency of trying to fix problems by throwing money at them. This led to them hiring a lot of mercenaries, most famously the Varangian Guard. The Varangian were drawn from among the Vikings including the Kyivan Rus.
But the Vikings were hardly the only Mercenaries the Greek-Romans employed, and they were even known to hire Latin mercenaries from Western Europe. This was what Emperor Alexios Komnenos was trying to do when he wrote to western nobles asking them to send soldiers.
Instead, Pope Urban II took the opportunity to whip up religious fervor and set in motion what are now known as The Crusades. Instead of small units of elite soldiers, happy to take the Emperor's coin and do his bidding, the Empire was flooded first with useless peasant crusaders, and then with organized armies led by haughty princes. These princes went on to carve their own fiefdoms out of the Levant, outside of the Emperor's authority.
But what if Urban hadn't done so? What if he had just let the nobles of Western Europe organize a small professional force, and blessed them on their way? How would history have been different?