Not at all knowledgeable in the political/military stuff about Alexander's conquest of India (I'm the modern Middle East history guy... sorta) but I'd love to see the cultural effects of it, there was a primitive Greco-Indian culture that flourished following Alexander's conquest as an after-effect, the death throes of a dead Hellenic empire. If Alexander had subjected a large amount of the kingdoms of India or gotten others to be vassal kingdoms of his empire it would have been interesting to see the cultural effects. Science-wise the world could have become way more advanced and the political spread of the world (i.e. what was considered the "known" world at the time) could have been largely expanded. For successor powers like Rome, places like India and China were profitable trade partners and routes that linked to their trade networks were IMMENSELY sought after in that era, that said, you might have a Rome that places more emphasis on expansion eastward than OTL, wars with the Parthians and the Seleucids would have been less of a half-assed every so often affair and something frequently done, either that or Rome would work for an alliance, because suddenly there's a lot more of the Asian trade to which Rome will have access thanks in part to Alexander's Empire.
I think this would still have the existence and flourishing of the Roman Republic, a more overextended Seleucid Empire might even make Rome stronger.