It's a bit off-topic, but read "Collapse" by Jared Diamond. Read it for its own sake. It includes examples of singularities successfully averted.
Most of my examples above are not so great; probably the global singularities in our past are actually limited to adoption of agriculture and, earlier, language, and the near-extinction event ca. 50K B.P. (maybe a climate-affecting eruption).
As noted elsewhere, a Vinge singularity is just an event after which the world becomes incomprehensible to someone raised before it occurred.