And yet they remain useful when conclusive evidence is not available:
Faced with the 1854 cholera outbreak in London, John Snow had no idea what mechanism caused cholera, and his instruments could not reliably identify the contaminants in water supplies, but he noted what we would now call correlations: some water companies had more of their clients die than others, even though all of them supplied to rich and poor households alike. South of the river companies were more deadly, and they drew more contaminated water from the river rather than other sources, and filtered it less than other companies. Some neighbourhood pumps had more deaths nearby than did others. This was a geographic form of correlation (now called a Voronoi diagram) and it was on that correlational basis, without knowledge of the real mechanism, that he took the handle off the Broad Street pump, and stopped the epidemic.
That is the way we tell the story now, but Snow was a careful and clever man, and pointed out another explanation: the cholera outbreak was coming to an end anyway, as people ran away from areas where there were many deaths. The common folk who believed that correlation implied causation ran for their lives and lived to see another day.
Snow also had to cope with a major anomaly in his geographic correlational investigations. None of the brewery workers right next to the Broad Street water pump fell ill with cholera. It turned out that they received free beer, and the water for the beer was boiled so as to release the flavour of hops, thus inadvertently killing off the water-borne organisms.
Snow jumped to a conclusion because his mind was prepared to interpret associations in a particular way, intially by his doubts about the air transmission miasma theory and later by his own hypothesis of water-borne transmission. He jumped to the right conclusion, without proofs of the causal mechanism which were only available years later.
This is why you should NEVER try to dismiss any correlation with the idiot’s refrain that “correlation is not causation”. That is an astonishingly stupid thing to say, as it is tantamount to saying that “a clue is not a mathematical proof.” Who claims that it is?
As Michael Woodley points out, there is never causation WITHOUT correlation. Which means that correlation is a necessary, but insufficient indicator of causation, it is not a synonym for it.