I've always loved the idea of a surviving Mughal Empire. The Mughals are my favourite Indian empire, not in the least because of the sheer cultural syncretism between Indian and Persian culture that happened in the time, and the great art forms that were created in the time period include works such as the Taj Mahal, and their wonderful miniature paintings. If its overexpansion under its Padshah Aurangzeb had been avoided, the Mughals probably would have survived, making the cultural bloom, as well as the art forms, of the Mughals permanent entities in India.
My other big idea is the Kushan Empire spreading Buddhism to the Roman Empire. The Kushan Empire were tremendously powerful, and were an Indo-Iranic empire as well, with many cultures existing in it, including Hellenic culture in Bactria. One Kushan god was Oesho, a syncretism between the Indian Shiva, the Persian Vata-Vayu, and the Greek Heracles. All in all, the sheer syncretism of the Kushan is amazing. They are also recorded as having traded with Rome tremendously, as shown by the high amount of Roman coins in this time period. The Kushan emperor Kanishka the Great is also responsible for sending Buddhism across East Asia. If he had sent missionaries to Rome, I think Buddhism would mesh well with Neopythagoreanism and Neoplatonism on the upper levels. On the lower levels, it would convert poor people due to the Buddhist emphasis on charity, and as a result, Buddhism would become a prominent Roman religion.