Placement of variables in a correlation

Lung cancer correlates with smoking. Smoking correlates with lung cancer.

Are both correct or does one have to worry about which one is the dependent variable (lung cancer) and which one is the independent variable (smoking)?

"Correlation does not imply causation" and if your listener understands that then you can use it in either order. From xkcd:

But if they do not understand, and instead think correlates with is similar to is caused by then you might try to put what you think is the effect before the cause.

Both are correct. Wolfram MathWorld defines correlation as

...the degree to which two or more quantities are linearly associated.

Perhaps you are concerned that the order in which you talk about the variables will alter their correlation. MacMillan Dictionary's definition of correlation may clarify:

correlation: a connection or relationship between two or more things that is not caused by chance. A positive correlation means that two things are likely to exist together; a negative correlation means that they are not

Smoking correlates with lung cancer and lung cancer correlates with smoking are positive correlations in either case. If you smoke, it's more likely that you will develop lung cancer; if you have lung cancer, it's much more likely that you were or are a smoker.