Most Significant Event in History from 1000 to 1500 C.E.

I would generally point to Columbus's voyage. Certainly most of these events are connected in form or another, but we can't say for certain that the alternate course of history (if some of these events would not have happened) would not have led to a roughly similar turn of events in the grand scheme of things. The balance of power in the Eurasian/North African world changed all the time: whether one region or another was dominant is important but not essential.

Columbus' voyage is crucial though because it opened up another world, with its economic resources, new food sources and new opportunities. Just compare it with some of the other events: is a Europe with a large and strong Byzantine Empire really all that different from a Europe with a large and strong Ottoman Empire? Is the balance of power in Eurasia after the collapse of the Mongol Empire in the mid 14th century all that different from the balance of power in the early 13th century, before the Mongol invasions? Sure, there are differences, but in the overall scheme of things, it doesn't really matter whether Europe or China is somewhat stronger - there is still a certain balance along the same old lines... The world is different but it's still the same "size". Columbus' voyage however is a sort of paradigm shift: the world itself got bigger.

This being said, there are other events which deserve a special mention (in no particular order:

1. the schism of 1054, without which the 4th crusade and the weakening of Byzantium would not have happened.
2. the black plague which depopulated Eurasia
3. the Reconquista in Spain and Sicily (another contributing factor to the Renaissance and the voyages of discovery)
4. the great economic boom of Song China, which resulted in the general revival of the economies of all of Eurasia - the 12th century Renaissance in Europe would scarcely been possible without it, with everything which that entails.
5. the muslim invasions of India which altered India's role as an economic and cultural dynamo of the world, and brought India within the Middle-Eastern ann European world.
6. The rise of great trading powers in Western Africa (Ghana, Mali, Songhay) - which fueled Europe and the Middle East with the gold necessary for their economies.
7. The conversion of the Russians to Eastern christianity, and the destruction of Kiev by the Mongols (as opposed to say Moscow). These two events shaped Russia into an agricultural country (as opposed to commercial had Kiev stayed strong), and an Eastern Orthodox as opposed to Muslim. Can you imagine a commercial, muslim Russia?
8. The fall of the Khmer and Majapahit Empires, which relegated the potentially central region of South-East Asia, at the cross-roads of trade, to a region somewhat marginal.
9. The rise of the Incas in Peru: imagine what would have happened if a universal empire did not exist in the Andes at the time of Pizarro's conquest, and if the conquistadors could not have used the conquered peoples' hate against the Incas.
10. The rise of the Aztecs in Mexico: same reasoning as number 9 (just substitute Cortes).
11. The condemnations of Paris in 1277, which eventually resulted in a great shift in European philosophical and scientific thinking, by forcing a move from Aristotlenianism.