Something we should consider, whenever we investigate ideas as broad and fundamental as these, is that topics relating to crime, justice and society have been discussed for thousands of years. Therefore, there has been no consensus or "right" answer in the objective sense. Often, when it comes to these subjects, it's easier to reflect on what is and has been, rather than to predict or prescribe action against what might be. Thus, considering the relationship between societal attitudes and the definition of criminality is a good application of rhetoric. However, we may find the means of acting upon our findings to be limited.
Crime is by definition an action that violates a law; however, law can be agreed upon in a democratic fashion where it reflects the will of people governed by that law, or it can be handed down from a superior authority, such as a king or a court, in which case it may not reflect the will of the people. Likewise we might consider that laws do not impact all persons equally, and laws that one might consider just could be unjust to another.
The point is that the concept of "criminal behavior" is likely to be relative to the time, place and person; societal attitudes about cars would be nonexistent 200 years ago, and a modern-day person would be hard pressed to care about parking laws and traffic tickets. The same goes for the flip-flop in criminality that the United States underwent regarding alcohol in the 18th and 21st amendments. We could look at innumerable examples, but I don't think this kind of pedantry would be very informative. It seems fairly self-evident that basing criminality merely upon the existence and applicability of a law is far too arbitrary. More specific examples can be found in cases of jury nullification, in which the jury during a criminal trial determines that the law the defendant is accused of breaking is, itself, unjust.
Instead, could we consider something more "universally" criminal? The question asks us to consider "behaviors that society considers criminal" - so we might look to examples of behaviors that all societies consider criminal. These would involve crimes such as murder and theft; many of the "laws" that these would violate are considered fundamental human rights, one example of which may be found in the United Nations document titled The Universal Declaration of Human Rights.
Are there examples of societal attitudes flipping a fundamental action, such as murder or theft, from criminal to non-criminal, or vice versa?
I think it would be difficult to argue that, when this occurs, the society in question is not conscious of the reversal, particularly if it happens in a very short time. For example, upon declaration of war, murder suddenly becomes not only non-criminal, but desirable, if it's directed at the enemy. In this situation the society in question may argue that the reversal is justified by the fact that the society itself is endangered, and is acting defensively. Being able to define actions as criminal might then be seen as a luxury of a society that is not actively under threat from outside.
We can follow this line of thinking to the conclusion that crime is whatever the society considers to be destructive to itself. This will, naturally, change over time. A society barely scraping an existence from a resource-depleted region will naturally have fewer petty bureaucratic considerations than one that is successful and focusing upon the details, such as where you park your car.
Another insight into this question may be found in Kohlberg's Stages of Moral Development, and the Heinz Dilemma often used as an example of those stages. The dilemma invites judgments such as whether we should consider a crime to be more or less criminal based upon the reasons for which it was committed; does theft, to save a life, deserve the same treatment as theft to serve one's own greed? I think many people would argue that the former situation is a less criminal one, even though it may fulfill the same impersonal definition of criminality.