What sort of mythologies/religions existed in antiquity/classical Asia? As in, before Taoism and Buddhism became very widespread, was there any sort of established pantheon like in Greece or Egypt, or was it more tribal like northern America or Africa?
Asia is a huge, huge place. There were a wide variety of religious practices. Bear in mind that all of the world's most practiced religions today, originate in Asia. India, China, Siberia, the Middle East, and the Central Asian steppe are all very different places with very different histories. Is there a particular part of Asia you're interested in? Also, what do you mean by antiquity? Because the Tao Te Ching dates to at least the 4th century BC, and Gautama Buddha lived most likely somewhere between the 4th and 6th century BC.
(I'd also point out that while Taoism and Buddhism are widespread, they are neither the most widespread or most popular "religions" in Asia today. Islam has the most adherants in Asia, and Hinduism the second-most.)