This video showing the spread of religion on Business Insider is pretty interesting. My takeaways were that it's great to be the religion of a spreading empire (Roman/Spanish for Christianity) and Islam was spread on the basis of sea trade.
But the spread of Hinduism went to the eastern borders of India and was eventually checked by the rise of Buddhism. Why didn't Hinduism spread more or into the Middle-East?
Link to BI article: http://www.businessinsider.com/map-shows-how-religion-spread-around-the-world-2015-6
Don't believe everything you see on the Internet. That map is remarkably bad. For one, there's a rather big debate about whether the Indus Valley civilization was Hindu. I believe the consensus among secular scholars in the West leans away from that perspective (though it is still popular in India). Many Hindu gods generally have equivalents in the Indo-European pantheon (and there's particularly close ties between early forms of Hinduism and early forms of Iranian religion that eventually developed into Zoroastianism). It's unclear what language they spoke in the Indus Valley, but it almost certainly wasn't an Indo-European one. We know little of the details of their religion, however, because the script remains undecipehred.
Hinduism spread all the way to Indonesia by the 9th century CE. The island of Bali is still majority Hindu, but most of the archipelago was, too, at one point. Look at the Prambanan temple complex outside of Yogjakarta as a testament to Hinduism influence in this period. (Buddhism also had a strong presence for much of the pre-Islamic period as well, often in competition with Hinduism for patronage among the various kingdoms--witness the massive temple complex at Borobudur, for example.) The first time I saw the Ramayana performed was in Indonesia in Indonesian. And it wasn't just Indonesia either, but really the whole area between India and Indonesia that was under the influence of Hindu civilization. The famous Ankor Wat temple complex was founded as a Hindu temple and only gradually became a Buddhist temple (as a side note, this sorts of mixing are common among most religions--the "jealousy" of Judaism, Christiantiy, Zoroastrianism, Islam, etc. are the exceptional ones, not the mixing style of Hinduism, Buddhism, Shinto, Chinese folk religion, etc.).
But, in short, that map just isn't very good. There are a lot of misleading elements and outright errors in it.