The 4th Crusade had some very important consequences, the most significant would likely be the drastic weakening of the Byzantium Empire, which led to the rise of the Ottoman Empire. Constantinople had been a bastion of the Christianity and an extremely wealthy city, but the 4th crusade devastated the city. The empire, and the city itself had become a shell of its former self, and was unable to quell the rise of the Ottomans and eventual takeover. The city was so depopulated that when Sultan Mehmet conquered it, he had to force citizens to move their from the Balkans and Anatolia.

Many historians believe the influx of refugees from the fall of Constantinople is what led way to the Renaissance. Furthermore, the Ottoman cartel on the spice trade also led the European states to look for alternative trade routes, eventually finding the new world.

Source: The Fall of Constantinople, Being the story of the 4th Crusade by Edwin Pears.

Edit:grammer

It certainly is hard to argue against the idea that one of the consequences of the 4th crusade is a weakened Byzantium, thus contributing to the rise of the Ottoman Empire. I do quibble with idontIikecats assertion that it "led to the rise of the Ottoman Empire" rather than being one of many factor.

More important would be the battle of Manzikert in 1071 in which Arp Arslan defeated Romanos Diogenes and triggers a civil war between Doukas and Diogenes. This allows the large scale settlement of central and eastern Anatolia to the Turcoman tribes. The Turkish tribes made it all the way to Nicaea by 1075-1077 and made it the capital of the Seljuk Sultanate of Rum state. There is some back and forth between Byzantium and the Seljuks over the ensuing years, but attempts by Manuel I Komnenos 100 years later to recapture central Anatolia also failed, and let the Turks solidify their position in western Anatolia. Byzantium was left with only a slight hold along the Aegean coast.

The defeat of the Seljuks by the Mongolian Ilkhanids destroyed the Seljuks in Anatolia, the most notable victory being the battle of Kose Dag in 1243. The Ilkhanids were not much interested in Eastern Anatolia and the power-vacuum between the Byzantine and Ilkhanid lands led to the rise of small, competing Turkish marcher states, of which the Ottomans were one.

The collapse of the Byzantines was death by 1000 cuts, and Byzantium was already in steep decline at the time of the 4th crusade. Conflict in Anatolia, revolts in Bulgaria, Serbia, invasion by William of Sicily and internecine struggle all weakened Constantinople directly prior to the 4th Crusade...in fact this weakness is probably what made it such a tempting target.

I think that the rise of Venice and its territories in the Aegean and Black Sea are more directly linked to the 4th Crusade. Indeed it was primarily the work of Doge Dandolo that the crusaders were diverted to take Christian cities of Zara and then Constantinople.

sources: primarily Osman's Dream by Caroline Finkel.