Some creative ones...
1st century - A civil war in the Roman Empire results in Egypt reemerging as the "Southern Roman Empire"
2nd century - The Yayoi are introduced to Chinese culture, religion, and literacy. Eventually *Japan extends nearly to the Aleutians.
3rd century - Persia is able to conquer the entire Arabian Peninsula and expand into Africa, the Levant, and Cyprus.
4th century - Java's Tarumanagara kingdom commissions an exploration of the eastern islands, discovering Papua and Australia.
5th century - Permanent Hunnic Empire controls much of continental Europe indefinitely.
6th century - Avar Khaganate leads to a permanent Turkic presence in Central Europe.
7th century - Tibetan Empire solidifies control and possibly expands into China proper.
8th century - Abbasid Caliphate converts the Norse to Islam via the Volga trade route, establishing a multiethnic Muslim empire along the Baltic shores.
9th century - Ghana Empire discovers the Canary Islands, Cape Verde, and Madeira.
10th century - Greenlandic Norse expand beyond Newfoundland, sailing as far south as Florida. Exposure to European diseases means that Amerindians are more than ready to fight back and, better yet, the fabulously wealthy Aztec Empire charters an expedition to their homeland (Europe) in the 1480s, resulting in a Sunset Invasion.
11th century - Mapungubwe expands southwards into the Khoisan lands, eventually unifying Namibia and South Africa.
12th century - Jürchens not only take China but push into Siberia, discovering the New World.
13th century - Slave Dynasty India expands ties between South and Central Asia.
14th century - Mali Empire uses its insane wealth to focus on maritime navigation and permanently establishing Mali as a great kingdom, circumnavigating Africa in the 1310s.
15th century - Janjira (or the Siddi/Africans of India in general) is able to carve out a large principality on the west coast of India that eventually becomes a sovereign state a la Sri Lanka.
16th century - Protestant European forces are able to make a tentative alliance with the Ottomans to tag-team the Catholics. Vienna, Munich, and Leipzig all fall to Turkish forces.
17th century - Barbary pirates, similar to the 16th century scenario, are able to establish a foothold on the European continent.
18th century - Nueva España is granted independence shortly after the US is, and the mestizo state upstages the US as the greatest power in the New World.
19th century - French Louisiana gets its independence instead of being sold to the US, and the mulatto state upstages the US as the greatest power in the New World.
20th century - The British choose to develop Somaliland as the Singapore of Africa.