An alternate world stemming from Emperor Frederick crowning Charles the Bold as an independent monarch at Trier in 1473. Charles won the Battle of Nancy with significant aid from the Emperor.
Burgundy's relation with the Holy Roman Empire began to sour in the 16th century, but by that time, they had conquered much of France (with English aid), and secured themselves against any hostility from the east. After the Florentine explorer Amerigo Vespucci discovered the great western continent that bears his name, Burgundy, along with England, Spain, and Sweden, was eager to plant overseas colonies. At one point, they controlled much of America.
Spain, overextended in the New World, and coming out of a disastrous war with Burgundy in 1590, fell prey to an Ottoman invasion in 1591, following on their occupation of most of southern Italy. The Pope fled to Burgundy and was eventually granted Avignon as his personal fief. Spain, then Portugal, fell to the Ottomans, and the monarchs of both those nations fled abroad, eventually settling in their still-prosperous New World colonies.
During the 17th centuries, a series of succession wars led to the formation of two great new powers in Europe: the Union of Four Crowns, comprised of England, Scotland, Ireland, and Denmark, and the Imperial Union of Scandinavia, made up of Sweden and Norway. The Scandinavians especially were a force to be reckoned with, allying themselves with the Ottomans against the Russian Empire, and conquering vast tracts of that country in conjunction with the Ottoman armies. Eventually Scandinavian power began to wane after a series of weak monarchs, but the damage was done to Russia; hemmed in by powerful enemies, she was destined to remain a second-rate power.
As European explorers spread far and wide, eventually contact with India and the Far East was made. India came to be dominated by Burgundy, and to a lesser extent, the Four Crowns. China, too vast to conquer or vassalize in its entirety, began to adapt Western philosophies and technologies. By the end of the 18th century, it was a power as great as any other on the planet, controlling nearly half of Asia, most of the Pacific, and a large colony in America.
Meanwhile, in America, independence movements began to spring up like brushfire. Unlike OTL, colonization of America (OTL North America) spread from east, south, west, and to some extent north, fairly equally, creating a huge zone in the Great Plains where dozens of cultures met, clashed, and eventually formed into something greater than the sum of their parts: the Union of America. Since then, America has grown into one of the world's great powers; due to this nation's radically different origins, race has never played a great part here. People of all creeds and colors are welcome, for the most part. Though there were still great die-offs amongst the natives, the survivors have integrated much more fully than OTL.
There are also two great success stories: the Haudenos League, and the Tsalokai Union, two strong native states. Since the end of the Second Great War in 1937, there's been talk of the League joining the American Union, and now with the Ottoman Alliance prepping for yet another clash with the West, it seems that possibility may become a reality.
In China, more than two centuries of modernization have still not guaranteed equality for all her citizens; this has led to a bloody civil war concentrated in the south. While China fights itself, her central Asian satellites have begun to break away, aided by various powers, most notably the Ottoman Empire and Russia.
Africa has turned out quite a bit better than OTL; though large areas are still European colonies, the standards of living are on the whole much better, and most lands are on track to be decolonized by 1965 - assuming the Third Great War doesn't end civilization beforehand...