The big one coming up is going to be massive technological failure: so strong that it will undermine faith in science for a generation or more.
It's going to happen because science is expanding at a fast rate, and over the past few centuries, the more science we've had, then — albeit with some time lags — the more powerful technology we have had.
That's where the problem will arise. With each technology, the amplitude of its effects gets greater: both positive and negative. Automobiles, for example, are an early 20th century technology (based on 18th and 19th century science), which caused a certain amount of increased mobility, as well as a certain number of traffic deaths. The amount on each side was large, but not so large that the negative effects couldn't be accepted. Even when the negative effects came to be understood to include land-use problems or pollution, those have still generally been considered manageable. There's little desire to terminate all scientific inquiry because of them.
Nuclear power is a mid 20th century technology (based on early 20th century science). Its overall power is greater still, and so is the amplitude of its destructive possibilities. Through good chance its negative use has, so far, been restricted to the destruction of two cities. Yet even that led to a great wave of generalized, anti-scientific feeling, not least from among the many people who'd always felt it's impious to interfere with the plans of God.
The internet is any many ways an even more powerful technology (based on early 20th century quantum mechanics, and mid 20th century information theory). So far its problems have been manageable, be those in surveillance of personal activity, or virus-like intrusions which interrupt important services. But the internet will get stronger and more widespread, as will the collaborative and other tools allowing its misuse: the negative effects will be greater still.
Thus the dynamic we face. Science brings magic from the heavens. In the next few decades, clearly, it will get stronger. Yet just as inevitably, some one of its negative amplitudes — be it in harming health, or security, or something as yet unrecognized — will pass an acceptable threshold. When that happens, society is unlikely to respond with calm guidelines. Instead, there will be blind fury against everything science has done.