Christianity arguably would not be as big as it is now if not for:
War - the European Christians conquering other countries in war, colonizing them and then imposing Christianity.
government support - the Romans made Christianity the official religion of the empire which allowed it to conquer Europe
Islam would not be as big as it is now is not for:
War - the Islamic conquests after the death of Muhammed spread Islam far and wide
government support - countries that have a majority of Muslims tend to make it their state religion which ensures that Islam spreads
Buddhism also would not be as big as it is today if not for:
government support - the Chinese and Indian (Ashoka the Great) emperors that spread Buddhism ensured that it would be adopted far and wide by giving it their seal of approval
In conclusion, the big religions of today are only big because they were forced upon a lot of people. The local religions stood no chance as their people simply weren't strong enough to resist these larger religions.
