I think avoiding the World War I is impossible.
I disagree with Jared in that the black death allowed industrialization to happen. It improved the lot of the peasantry by causing an increase in the demand for labor, and gave them bargaining chips against the feudal aristocracy. Without it, peasants would be kept under the boots of the nobility for some time, none of which adds up to earlier industrialization by my reckoning.
Perhaps the English winning the Hundred Years war decisively. They rule France for two hundred years, eventually being driven out by the unified Spaniards or somebody else.
With France gone, or divided, or something, colonization of the New World takes much longer, as the nations of Europe have something to fight over, thus leaving them in a perpetual state of war over the lands of France.
This would also likely lead to a faster consolidation of Germany. German states would inevitably find themselves at war with one another and with the duchies in France, and against larger states like England/Great Britain. This would lead to consolidation through conquest or alliance. The larger states would invariably come to dominate the various smaller ones, and I think we'd have a few power blocs by the 1750s, around Prussia, Bavaria, and Hanover or Mecklenburg. These states in turn would fight a long series of wars for domination of the German states, including the Hapsburgs, who would likely envelop Bavaria. This would leave two states in Germany, Prussia and Hanover, and Prussia would probably win.
You'd probably get a 20th Century free of world wars, as Europe would be too busy fighting itself as France fights to unify, Prussia and Austria battle it out, England seeks to keep France disunited, and Russia expands in all directions, mainly west....
