Correlation does not imply causation, as there could be many explanations for the correlation. But does causation imply correlation? Intuitively, I would think that the presence of causation means there is necessarily some correlation. But my intuition has not always served me well in statistics. Does causation imply correlation?
As many of the answers above have stated, causation does not imply linear correlation. Since a lot of the correlation concepts come from fields that rely heavily on linear statistics, usually correlation is seen as equal to linear correlation. The wikipedia article is an alright source for this, I really like this image:



Look at some of the figures in the bottom row, for instance the parabola-ish shape in the 4th example. This is kind of what happens in @StasK answer (with a little bit of noise added). Y can be fully caused by X but if the numeric relationship is not linear and symmetric, you will still have a correlation of 0.

The word you are looking for is mutual information: this is sort of the general non-linear version of correlation. In that case, your statement would be true: causation implies high mutual information.
