Does correlation correlate with causation? Correlation does not imply causation, but causation causes correlation. By correlation I do not mean exclusively linear correlation, it could be arbitrarily shaped, as long as it is consistent and reflects dependency.
Does correlation correlate with causation?
At first I thought: "Yes, because every causation implies correlation hence there definitely is a correlation between correlation and causation."
But then I thought: "Wait, the answer is no because for every correlation that is truly causal there are an infinite number of correlations that are not causal, hence the correlation between correlation and causation is not significant."
Which is right, the first answer or the second answer? Or neither?
 A: The sentence "correlation does not imply causation" is usually understood much broader than it should be. If two variables A and B are highly correlated, then something is causing something else. You just cannot conclude that A causes B because there are a number of other possibilities:


*

*B causes A

*A and B are both caused by C

*Only if D is given, does A cause B

*A causes E which in turn causes B

*(An error of type I occured and the correlation is not significant, but this one is dealt with by talking about strong correlations.)

A: 
Does correlation (any statistical association) correlate with (related
  to) causation?

This question (words in parentheses are mine) is quite general and essentially the answer seem me yes. Causal inference in statistics framework exist exactly because the answer to that question is yes.
However in order to give more useful answer we need to better specified question. The following question seem me the best:
Does causation imply correlation?
This question already exist in this site and several interesting answer are given. Read here:
Does causation imply correlation?
others related questions are:
Under what conditions does correlation imply causation?
Statistics and causal inference?
Regression and causality in econometrics
A: Correlation is a special type of association and association is different from causation which can be only inferred from a randomized experiment(the reason would be the confounder). 
References:
1. Association and Correlation
2. Openintro-Statistics
