Converse Error

Has nothing to do with shoes.

Affirming the consequent

This claim is most simply put as:

If A, then B.
B.
Therefore, A.

It's a fallacy because at no point is it shown that A is the only possible cause of B; therefore, even if B is true, A can still be false. For example:

If my car was Ferrari, it would be able to travel at over a hundred miles per hour.
I clocked my car at 101 miles per hour.
Therefore, my car is a Ferrari.

This is popular in conspiracy theories. Here the fallacy is fairly obvious; given the evidence, the car might be a Ferrari, but it might also be a Bugatti, Lamborghini, or any other model of performance car, since the ability to travel that fast is not unique to Ferraris. Hell, it might even be a Subaru Outback. Note that while this may appear to call all hypothesis / evidence experiments fallacious, they are based on additional evaluations of the likelihood of other theories, thus establishing that A is a likely cause of B.

Denying the antecedent

The flip side of the above, where you say that because the initial conditions did not happen, the result is impossible.

If a person is wearing a hat, they have a head.
I am not wearing a hat.
Therefore I do not have a head.

Note that, by the contrapositive rule, these two fallacies are equivalent. For example, you could replace "If a person is wearing a hat, they have a head" by the logically identical statement "If a person has no head, they aren't wearing a hat" to turn the first example of denying the antecedent into an example of affirming the consequent.

Looks like this fallacy but is not

Inference to the best explanation. The usual form of scientific reasoning, as well as a lot of Sherlock Holmes' "deductions" (though he's wrong to call them that, since this is a form of inductive reasoning).

B.
The best explanation for B would be A.
Therefore, A (probably).

- This differs from the Ferrari example above in that it posits a stronger connection between A and B than just A's truth entailing B's; B is actually giving some positive reason to prefer A over the other possibilities. (This approaches, without actually becoming, the logical relationship "if and only if".) Also, this form of argument isn't claiming deductive certainty, so the bar is a little lower for it being acceptable.
- Scientific reasoning is frequently attacked by those who understand this fallacy, but not the scientific method, which has the following form:

B.
A is the best explanation for B, so I will claim "A is the most likely explanation."
If A, then C.
Therefore, if not C, not A (valid contrapositive).
Is C true? Yes? I will increase my confidence that A is the correct explanation.
If A, then D.
Not D!
I must provisionally reject A or modify it to account for D, then continue to seek new information and propose new possible explanations.

Examples of Converse Error include:

In American Dad, Stan sinks his entire savings to build a rocket for Steve to win a contest.

Stan: You gotta spend money to make money.
Francine: But you didn't make any money!
Stan: So logically, I didn't spend any money! *waves at the camera* Goodnight everybody!

An argument made by Obama supporters against conservatives.

Racists who don't like black people oppose Obama's presidency
Bob opposes Obama's presidency
Therefore Bob is a racist.

- This is not to say that you can't make an argument that someone that opposes Obama is a racist, but it does not follow automatically from being opposed to his presidency and/or policies.
- A similar argument from Obama detractors is that anyone who voted for Obama did so only for affirmative action's sake, rather than because they believed Obama was a strong candidate on his own merit.
- I opposed Obama because I was for Hillary, you sexist!