1) The Pure Soul Rebellion.
In 762, a descendant of Ali and Fatima named Muhammad ibn Abdullah raised the standard of rebellion along with his brother Ibrahim in Medina against the newly instated Abbasid Caliphate. The Abbasids claimed a right to the Caliphate as they were related to the Prophet, but some said that the Alids had more of a claim. Muhammad and Ibrahim exploited this and began rebelling against the Caliph Al-Mansur. Medina was not a good choice for a base, as it depended on other provinces for goods. Muhammad raised a large but rag-tag army, and they overthrew Medina. The Abbasids responded by cutting of supplies and sending an army. Many encouraged Muhammad the Pure Soul to flee to Egypt, a better base or to the Banu Shumayma which had the most horses in Western Arabia. Muhammad stubbornly stayed at Medina, the home of his ancestor, and in the fashion of the Prophet dug a trench around Medina to protect the city. The trench was overcome, and all of the Pure Soul's supporters perished in the fighting.
What if Muhammad had fled to Egypt or some other province or the Banu Shumayma. What would happen. He could have garnered much support as many were disappointed that the Abbasids did bring to power the Family of the Prophet.
2) The Rashideen
Basic premise is that Uthman does not get assasinated. The bands of rebels coming from Egyp led by Muhammad ibn Abu Bakr and Muhammad ibn Hudhaifa camped in Palestine before going on towards Medina. Muawiya, Marwan and other governors asked permission to attack them, but Uthman refused thinking he could solve it all with words. What would have happened if he allowed, and Uthman's reign continued on. Reports were that he was making preparation to attack Constantinople.
3) Golden Horde Europe
Genghis Khan doesnt die, and Subutai continues onwards to take most of Eastern and Central Europe. Afterwards, this region turns into the Golden Horde, converts into Islam, and you now have a Mongol-Islamic presence in Europe.
4) Ottoman Central Asia
The Ottoman Empire doesnt attack the Mameluke empire, but focuses its directions on Iran, after conquering it the move into Central Asia, to create a mostly Turkic Empire. Meanwhile the Mamelukes experience a flourishing and become a powere to rival that of the Ottomans.