My all time favorite is to present correlations as causations.

See the example below.

(Image Credit: Lose pounds by eating cereals twice every day)

Given article talks about a study, that researchers at Oxford Brookes University discovered that after two weeks, 85% of people involved in the study had lost more than four pounds in weight.

How the article is presented on the newspaper suggests a causal relationship. That is, eating cereals twice a day causes losing weight.

Wait before you hit the nearest store and buy packages of cereals!

We cannot talk about a causation here, there is at most a correlation. Meaning that if people who eat cereals twice a day loses weight, it does not mean that eating cereals is the reason that they lose weight. There must be another variable, like being health conscious, that affects both sides of the equation. Health conscious people eat cereals twice a day because they think it is healthier. Similarly, health conscious people are careful about their diet overall, that is they work out, they drink a lot of water and avoid high-calorie desserts, so they lose weight.

And there is not always another variable around! For a very good example of that, see below. There is a correlation between number of people drowned by falling into a pool and number of films Nicolas Cage appeared in. Of course these two statements do not cause each other in any way possible, plus there cannot be another variable they affect both of them.

(Image Credit: http://www.tylervigen.com/spurious-correlations)