If we are talking about fame in the non-academic world, I would argue that the most famous ruler of the Assyrians was Sennacherib II. Sennacherib is famous for two reasons. First, his wars against Judah are mentioned in the Bible. Second, he is mentioned in a famous poem by Lord Byron called "The Destruction of Sennacherib." These sources make him better-known to the average person than most rulers of Assyria.
In history books, the most famous Assyrian rulers are Tiglath-pileser I and Ashurbanipal. Tiglath-pileser is credited with being the first to truly expand Assyrian Power and to create a true empire. Ashurbanipal is famous for being one of the strongest of the Assyrian rulers, but also one of the last to reign over the empire before it began to fall apart.