Generally, in my experience, most natural disasters in the ancient world were absorbed pretty easily by the inhabitants, and did not have massive effects on the overall course of events. Some cities were destroyed, many, many people died, but generally, in any given earthquake, for example, the cost was absorbed and life continued on.

In fact, the Levant (modern Israel and Lebanon) was so prone to earthquakes in the Bronze and Iron Ages that the ancient Phoenicians developed architectural techniques to help buildings withstand minor earthquakes! What they would do is use wooden beams every three or so courses of mudbricks to provide cushion when the earth was shaking. The extra flexibility of the wood helped the buildings to withstand minor earthquakes that normal, straight-up mudbrick buildings couldn't. You can see some of these techniques reconstructed at the site of Hazor in this photo.

However, this is not to say that some ancient disasters didn't affect the ancient world. Two disasters in particular spring to mind, the eruption of the Thera (Santorini) volcano, which scholars believe disrupted the economy of the Minoans and may have contributed to their downfall, and the drought which contributed to the Late Bronze Age collapse of such once mighty civilizations as the Hittites, Cyprus, Ugarit, the Canaanite city-states, and even Egypt all suffered major setbacks.

The Santorini eruption was not the direct cause of the Minoans' demise, since they were able to prepare for it (no bodies have been excavated, though many buildings were), and there is clear evidence of Minoan settlement above the level of the eruption. However, tsunamis destroyed a number of coastal towns (and the Minoans were a coastal-based civilization) and earthquakes related to the eruption also had an impact. However, it is still highly debated as to the actual extent of the role of the eruption in the fall of the Minoans.

The drought at the end of the Bronze Age is pretty severe and credited with seriously affecting the course of several civilizations. The exact cause of the drought is hotly debated, with opinions ranging from global-level climate change processes including orbital forcing (Wanner, Heinz, Jürg Beer, Jonathan Bütikofer, Thomas J. Crowley, Ulrich Cubasch, Jacqueline Flückiger, Hugues Goosse, et al. 2008. Mid- to late holocene climate change: An overview. Quaternary Science Reviews 27 (19–20) (10): 1791-828), atmospheric circulation patterns (Enzel, Yehouda, Revital Bookman (Ken Tor), David Sharon, HaimGvirtzman, Uri Dayan, Baruch Ziv, and Mordechai Stein. 2003. Late holocene climates of the near east deduced from dead sea level variations and modern regional winter rainfall. Quaternary Research 60 (3) (11): 263-73), anthropogenic deforestation (Litt, Thomas, Christian Ohlwein, Frank H. Neumann, Andreas Hense, and Mordechai Stein. 2012. Holocene climate variability in the Levant from the dead sea pollen record. Quaternary Science Reviews 49 (0) (8/23): 95-105), and potentially even fallout from the Santorini eruption, which is believed to have affected climates across the world, according to tree ring data in Ireland.

The drought gets my vote as the biggest natural disaster that greatly affected history. Without it, you don't have the collapse of many Bronze Age civilizations, and the rise of others (including the Israelites), which could potentially mean that without this drought, the Israelite kingdoms would not have formed and the Jews would not have become a major religion, and then Christianity and Islam would not exist. That's a big what if, and not particularly suitable for the subreddit, but I think the Late Bronze Age drought had a very significant impact on the course of history.

Does anyone have any good readings on the Krakatoa eruption? I'd love to read more about it, especially the global effects from an eruption of that scale.

I've linked to these papers before, but Chris Beekman and Alexander Christensen have suggested that a drought struck the Bajio region of north-central Mexico. This drought, which lasted several centuries, may have been the trigger for the migrations Mesoamerica experienced from the end of the Classic into the Postclassic. These migrations can be linked to the Toltecs, the later Aztecs, possibly the Epiclassic intrusion in Jalisco, and the migrants into Michoacan. 1 2

April 5–15, 1815, Mount Tambora in what's now Indonesia, brought on 1816, The Year Without A Summer. Disrupted monsoons devastated China & India. Snow lay on the fields in Massachusetts in July. The famines triggered in Europe contributed to unrest under the restored monarchies.

1588, after the Battle of Gravelines sent the Spanish Armada retreating north, the Armada Storm finished the job for the English and Dutch. A third of the Spanish ships never came back, preventing an immediate second attempt.

1274 & 1281, the kamikaze (typhoons), break Mongol assaults on Japan. The second fleet had over 140,000 men in over 4000 hulls.