A thumb & finger example: "If it's thumb, it's a finger. Therefore, if it's not a thumb, it's not a finger."
Edit:
There have been some answers rightfully pointing out that the example given above is not the best. So I'll add this quote from Alan Turing that, much better than my example, illustrates this fallacy.
If each man had a definite set of rules of conduct by which he regulated his life he would be no better than a machine.
But there are no such rules, so men cannot be machines
This is a case of Denying the Antecedent:
if P then Q
not P
Therefore, not Q
It is somewhat similar to the valid Modus Tollens:
if P then Q
not Q
Therefore, not P
There is rather more to this than saying it is an example of denying the antecedent. Denying the antecedent is exemplified by the form "If P then Q; not P; therefore not Q". Contrary to what the wikipedia page says, this is not always the same as "If P then Q; therefore if not P then not Q". This equivalence holds in the propositional calculus, but not in all formal systems. For example, it does not hold in logics with possible world semantics or in probability logic.
Also, strictly speaking, only formal languages can have formal fallacies. English is not a formal language, so any attempt to find a formal fallacy in it depends on assimilating the English sentence to a sentence in some formal language such as the propositional calculus. But any such assimilation is open to the challange that it is not a correct representation, or that the choice of logic is inappropriate to the task at hand. This is one of the reasons fallacy hunting is highly overrated and overused.
Furthermore, one should not forget that in ordinary discourse, the pragmatics of language is just as important as the semantics. Often when one asserts "if P then Q" it carries the conversational implicature "if not P then not Q". This was described by Grice, who distinguished conventional implicature from conversational implicature: the former is part of the meaning of the terms used and is not cancellable, while the latter is something conveyed by adherence to the cooperative principle and is cancellable. An example might be as follows: suppose Alice says to Bob, "if you wash my car I'll give you $10". Bob is entitled to infer in the circumstances that if he doesn't wash Alice's car, he won't get the $10. The whole point of Alice qualifying "I'll give you $10" with "if you wash my car" is to provide Bob with a motive to wash it. If Bob believes he will get the $10 anyway, he has no reason to wash it; Alice knows this and intends it when she makes her utterance. Alice could perhaps have chosen to say "if and only if you wash my car I'll give you $10" but in practice we typically don't bother to say this: we allow the pragmatics of language to do its fair share of the work of conveying the meaning.
Whenever it rains, earth moves on an ellipse with a radius of about 150 million kilometres around the sun.
Whenever it doesn't rain, suddenly the earth doesn't move around the sun anymore. Do you believe that? Does that make sense?
Various events have a correlation. The correlation is a measure how strongly one event happening goes together with the other event happening. (Importantly, correlation is not necessarily causation). Correlation is a number from 1 (events always without exception happen together or neither happens) to 0 (events are totally unrelated) to -1 (every time one event happens the other will not happen, and vice versa).
The fallacy would be assuming that any two events always have a correlation of 1, which is rarely true.
Your attempt to make an example of fallacy of the inverse is weak.
A reasonable being is obligated to read context into a statement.
The context of your statement is obviously:
"The odd looking things with joints sticking out from your palm".
Thus, "If it's not a thumb it's a finger" holds truth.
