The obvious instance of this would be Malthusean cycles in which the population would go through a period of growth, spurred on by previous depopulation or some new agricultural technique, before hitting the limits of existing agricultural capacity and collapsing again under plagues, famines and so forth. This would mostly represent extensive growth from there simply being more people, but of course more people could also mean more division of labor and specialization. The population growth of the Song and Ming Dynasties, for example, were matched by significant developments in the sophistication of commerce and industry. Often times, political developments could also spur a boom, such as the way the Roman conquest of the Mediterranean spurred economic integration, which could then unravel with the political order, such as the subsequent reversion to local autarky after the Crisis of the Third Century.

In a more abstract, generalized sense, Joseph Tainter has a theory of social complexity that is essentially a broad socioeconomic boom bust cycle. Essentially, societies will go through periods of growth and increasing complexity that expand the scope and sophistication of economic/political institutions, and the windfall from this increased complexity will be used to subsidize future growth. However, eventually a tipping point is reached where developing costly new mechanisms are needed to maintain the gains, putting societies into a vicious cycle where you have this complex system that people can't afford to maintain or allow to collapse. Eventually, though, collapse does come. To cite the Romans again, their initial growth was a self reinforcing cycle of plunder, economic integration and administrative sophistication enabling further plunder, economic integration and administrative sophistication. Then they reached a point where things started to backfire as these produced social conflicts, famines, plagues, institutional defects they couldn't deal with. In the short term they managed them by creating an incredibly top heavy and coercive administrative apparatus in the dominate, but in the long term that was even less unsustainable and led to an even more spectacular collapse later on.

For a contemporary example, modern industrial agricultural practices are unsustainable. However, if we were to immediately end them, the result would not only kill a lot of people, it would also probably be worse for the environment. So we have to develop new technologies to grow ourselves out of the problem, but these create even more issues and arguably exacerbate the underlying issue. So we're in a bit of a pickle.

Perhaps the most basic example is found in the new world agricultural communities - it was often the case that Iroquoian villages would amalgamate and grow to a (relatively) large size, essentially for reasons of protection (the larger the village, the greater its military worth) - only to use up the locally available resources, and shrink or move.

A recently discovered example is the “Mantle” site, near the present day city of Toronto:

http://asiheritage.ca/portfolio-items/the-mantle-site/

This Huron/Wendat village is the largest ever discovered: it seems to have developed and been abandoned over a generation or so. The assumption I have read from the site reports is that it was an example of a boom-bust cycle - boomed because of the need for protection; bust because of unsustainably.

It would appear that the lower the tech, the shorter the boom/bust cycle: new world cities often display this process (see for example the city of Cahokia).