Ignored explanations of the phenomenon in question. In many situations it is tempting to believe that because an explanation is consistent with the known facts it must therefore be the correct explanation. This is especially tempting when the particular explanation is the on which we would most like to be true (egs, Jesus returned in 1914. The Gentile Times start in 607CE. The last century saw more wars, famine, earthquakes, pestilence, and lawness than any other). However, this is wishful thinking and ignores the possibility of plausible alternative explanations of precisely the same observations.
The formal fallacy of affirming the consequent typically involves ignoring alternative explanations, as for instance in the following example:
If you accidentally expose your film, then your photographs won't come out. Your photographs haven't come out. So you must have accidentally exposed your film.
Here the numerous alternative explanations for the photographs' not coming out have been completely ignored: you could have had faulty film, they could have ben inexpertly developed, or perhaps you forgot to remove the lens cap.
When people are arguing from the existence of a correlation to a conclusion about a causal connection they are particularly prone to neglect the possibility of alternative explanations. For instance, a scientist attempting to show that musical ability is largely inherited might examine the musical ability of a large number of children of talented musicians and compare this with the ability of children from non-musical families. It would not be surprising in such a survey to discover a significant correlation btween a proficient musician and one or both of your parents being musical themselves. However, if the scientist were to take this as firm evidence of inherited musical ability this would be an unreliable conclusion to draw from this evidence alone, since children of musicians are far more likely to be taught to play a musical instrument from an early age than are other children. In other words, the scientist would be ignoring an alternative explanation of the same phenomenon. In fact, probably the most plausible explanation is that there are both hereditary and environmental factors in musical ability; this too is consistent with the observed facts in the imaginary case above.
People who believe that aliens from another galaxy regularly visit the earth, occasionally abduct people in order to perform medical experiments on them, buzz unsuspecting airline pilots and so on, usually maintain their exotic beliefs by ignoring the alternative explanations of the phenomena they take to be evidence for their beliefs. So, for instance, although it is undoubtedly true that strange patterns are sometimes found in cornfields, it doesn't follow that they must have been made by extraterrestrials. There is a wide range of far more plausible alternative explanations of the phenomenon, such as that they have been made by pranksters, or are the result of freak weather conditions. It is a huge and unwarranted step to move from the fact that such crop circles could have been caused by extraterrestials to the conclusion that the they must have been. Before reaching that conclusion you would have to prove that visits by extraterrestials are the only possible explanation, or at least the most plausible one, for crop circles. Only when we have eliminated other possible explanations should we believe the improbabl. And even then we should be aware of the power of wishful thinking.