What if the Empire had come out on top? After Canossa, Henry IV had so much going for him. What if perhaps in 1081, he installs his Anti-Pope, and Gregory is perhaps captures, and dies on time in the Empire's hands?
I would imagine if the Papacy had been significantly defeated the world would be fantastically different even in just a few hundred years. The Empire would be much more stable (easier crusades?), the Popes would be more under the control of the Emperor. Consequently, the Emperors wouldnt have to deal with all the meddling with their Prince-bishops.
Even more long term: the slow separation of church and state, would not happen quite yet. The kings would remain in effect, the heads of their national churches.
Ideas?
To win the Investiture Controversy the Empire needs the theocratic theory of Gregory VII to become heresy in the mainstream doctrine of the Church. Let's say the Emperor captures Gregory and most of the bishops loyal to him, has him deposed by a Council, and the Papal succession goes to a loyalist Imperial Antipope and his line. Gregory is put to death as an heretic and his ideas are condamned by the Council.
Effects: the Church redefines its structure and doctrine to be very similar to Orthodoxy, a separate body subservient and loyal to the secular state which does not mess in politics as long as a modicum of autonomy is granted. The throne is the unofficial supreme authority of the Church in ordinary matters, the Council is the official supreme authority in doctrinal matters, the Pope is inferior to both. The reform either never happens or it takes an Anglican slant, a reform enforced from on high.
This might lead to schisms further down the line when other monarchies war with the Empire and their pet Pope. This might especially lead to an an early establishment of a separate Church for the lands of the British monarchies, and give the British-Imperial wars a religious undertone.
Heretical movements get democratic underpinnings, as they must set themselves against the throne-church alliance.
The Emperor gains a lot of prestige, beings ecclesiastical nobles firmly under control and and is greately reinforced against secular nobles. As a result, OTL drive to feudal fragmentation is butterflied away and a contrary centralization drive is established. In 1-2 centuries, the HRE is established as a centralized hereditary monarchy.
Without the support of the theocratic Popes, the separatist city-states in Northern Italy are brought under Imperial heel. The Empire stretches from Flanders to Rome and steadily expands East and South, fully absorbing Bohemia, Pomerania, Silesia, as well as Southern Italy from the Normans.
With wealth from merchant cities in Low Countries, Hansa, and Northern Italy flowing into Imperial coffers, and manpower from Germany and Italy, the Emperor is the hegemon of Christian Europe, only rivaled by the (waning) Byzantine Empire and the budding English monarchy.
To the Muslim, it looks like Allah has turned His face on them, since Crusaders backed by Imperial power conquer Syria, Palestine, and Egypt. This also accelerates the Reconquista in the Hiberian peninsula, which will eventually end up claiming North Africa as well. The Muslim Golden Age is abruptly brought to an end as plundred knowledge is transferred back to Europe where in a couple centuries the marriage of rediscovered classical wisdom and Imperial prosperity will birth a new culture. The Byzantine Empire is given a new lease on life as Muslim pressure is pushed back to Mesopotamia and Persia.
France does not fare much better than Islam, as its budding national unification is stillborn as the country becomes the prize of the Two Hundred Yeas War contest between the Empire and the budding Anglo-Norman Empire, which in a couple of centuries absorbs Western France. The Lotharingian-Burgundian estate is likewise gradually absorbed in the Empire. The rest of France is a patchwork feudal mess of myriad principates who keep independent by balancing the influence of both great powers.
Iberia avoids the same fate when a fortunate series of wars and dynastic marriages, sooner after the Reconquista is done, unifies the various states of the Peninsula.
Europe suffers a serious onslaught in the 13th Century with the Mongol invasion. Poland, Hungary, and Bulgaria are wracked but the Two-Empires alliance is able to contain the invaders until they suddenly withdraw for their own imperscrutable reasons. In the wake of victory good feeling, reconciliation of the Western and Eastern Churches can be eventually accomplished. Another effect of the Mongol war is that the Byzantine are able to reestablish control over most of the Balkans while the HRE absorbs most of Poland and Hungary.