Edit: amazing responses, thanks all!
Well, the consensus is generally something like "it was the Sea People, but it was also a bit more complex". The Sea People raids leading to the collapse captures the imagination, yet the view of raids in the Levant being the sole reason is starting to fade a little.
Cline's recent book deals really well with this and I think reflects much of the scholarly consensus. He argues that it is not a simple explanation; that there was one cause leading to a collapse. There were a number of complex, intertwining factors at play in the last 50 years of so of the Late Bronze Age (See Cline, 1177 BC: The year civilization collapsed).
Certainly, the Eastern Mediterranean around 1200-1150 BCE did see large migrations and invasions, which are commonly attributed to the Sea People, though to it generally accepted that this this explanation of collapse is simplistic. There's certainly plenty of archaeological and textual evidence for attacks from the sea. For example, this is a letter from the king of Ugarit (coastal Syria-Palestine) to the king of Alashiya (Cyprus) reporting sea raids:
My father, now the enemy ships are coming (and) they burn down my towns with fire. They have done unseemly things in the land. My father is not aware of the fact that all the troops of my father’s overlord are sta-tioned in Ḫatti and that all my ships are stationed in Lukka. They still have not arrived and the country is lying like that. … Now, seven ships that are approaching have done evil things to us, now then, if there are any enemy ships send me a report somehow, so that I will know. (RS 20.238, from Schaeffer, Ugaritica)
While this is all very dramatic and interesting, they only really tell part of the story. It does not explain how these attacks could have caused the near total destruction of a system that had been flourishing for 300 years, at least, according to the Sea People model.
The LBA in the Aegean and the Near East was extremely integrated. An international trade network, and advanced diplomatic and legal systems had been established between the imperial powers that had worked very effectively for several centuries. War had largely been abandoned between the Great Powers. Yet with such an integrated system, the failure of one part may affect the others. During the 13th century BCE, there is evidence of natural disasters, famine and a reduction of trade. Beginning around 1250 BCE, there is evidence of very dry weather, which almost certainly would have caused crop failures (Langgut et al, Climate and the Late Bronze Collapse; Drake, The influence of climatic change on the Late Bronze Age Collapse and the Greek Dark Ages). It is also at this point that we also see the resurgent Assyrian empire, which began aggressive expansion in the last quarter of the 13th century (Grayson, 'The Synchronistic History' in Assyrian and Babylonian Chronicles). Diplomatic relations start to decline, moving away from a model of cooperation. A combination of these factors and the integration of the system led to system decline.
It is unlikely that the Sea People raids would probably not have been so destructive without the system already being in decline. The weakening structure probably gave opportunity to those who wanted to take advantage of the situation. It was most likely a destructive mix of natural disasters; climate change and resultant agricultural problems; trade interruptions and economic failures; and migrations and invasions.
I think Chris Harman does a fairly good job of trying together a lot of different theories to provide a suitable explanation in his work 'A People's History of the World'. Essentially, he argues that it was internal pressures and dynamics which weakened various civilisations and left them prone to a variety of external threats such as slight climate changes and foreign invasion. He actually takes a broader view than most, arguing that the Bronze Age Collapse is actually part of a larger trend he terms 'crises of early civilisation', pulling Mesoamerican and Indus cities into the mix, across a much longer period of time.
The gist of his argument is heavily indebted to Vere Gordon Childe and argues essentially that the various ruling strata of these early civilisation grew ever more exploitative and consumed greater portions of economic surplus. He points to the work of Kemp (Old Kingdom, Middle Kingdom and Second Intermediate Period) in detailing the growing consumption by the Egyptian court system and strain on agricultural resources as a chief piece of evidence. This in turn drove down living standards of the working population to the point where, despite some advances in bronze working, many craftsmen and farmers laboured instead with primitive neolithic tools and older techniques were used as last resort (e.g. plucking wool, per What Happened in History and Lloyd's Ancient Egypt: A Social History).
Related to this is a dynamic which Childe explains, claiming that early civilisations went through a lengthy period of stagnation during their 'peak'. While great monuments and other signs of civilisation certainly seem grand, advancement in science and technology was miniscule compared to the leaps of the early agricultural societies. What advances did occur, such as in pure mathematics and water wheels, were largely by peoples on the periphery of these large civilisations (Man Makes Himself). The theory provided is that the ruling castes, having turned to a strategy of intensifying work for labouring classes, had little need for investing time or resources into labour saving technologies. Bruce Trigger, for example, details the cease in advances made by Egypt during the Old Kingdom period as scribes and bureaucrats came to dominate surplus consumption (The Rise of Egyptian Civilization).
These weakened civilisation were hence more susceptible to those factors mentioned here by others, such as invasion and climate change. Harman also adds intensified social strife to this list of factors, using Mayan peasant revolts as a key example. Egypt and Mesopotamia are highlighted as odd examples where changes in the ruling layers of society and some development in trading meant that civilisation went through a period of turmoil, but then largely got back on track for several centuries more until the collapse came again, as the underlying dynamic had not changed.
Although some of this work is getting a bit long in the tooth now, and certain archaeological evidence has been disputed, to my knowledge no one has ever really overhauled any of Childe's or Harman's basic approach or overarching theories.
Follow Up: Are there any major natural disasters - volcanic eruptions, earthquakes, climate change, etc - that coincide with the end of the LBE? I think I remember reading somewhere that climate change was a potential culprit, as it's often a push-pull factor in migration/invasions.
This is a really great thread! What is the percieved origin of the sea people? Where did they come from? Black sea region? Do we know anything about them?