This is related to the more general concept of social contracts, states, power hierarchies, and such. There have been several philosophers who have thought a lot about this. A good starting point would be to check out Hobbes' Leviathan, but there are also the contemporary Two Treatises of John Locke which are somewhat of a contrast to that. Anther philosopher would be famously Kant with his Imperative.
From a 10.000 km perspective, the gist is this: without any kind of law or power structure at all there is no crime, since crime is defined to be something which breaks law. But in that state, humans fall back to a base behaviour which - depending on whom you believe - is less than savoury. If you believe Hobbes, this would mean that the "law" of strength would rule; stronger people would roam the lands and just take whatever they want; there would be no law in our modern sense, and hence no crime, but many people would be very very unhappy (or dead).
The next step would be for the strongest humans to become chiefs or kings - they would gather lesser people around them and rule them by force. They themselves would be outside of law; they would be the law-giver. In return, they would protect the weaker ones from other tribes. This can work, and has for many thousands of years, but is obviously a little fickle and depends a lot on luck, especially regarding the character of the chief.
More modern and arguably refined methods then include a proper, written law, with no person above it, and some kind of structure (e.g. separation of powers) to protect it from individuals.
Thus, all we have today in the civilized world, including law, power structures and so on, follows from the need to get away from a barbaric state of affairs.
To answer your question: no, directly speaking, except for the punishment attached to the laws, there is no particularly reason to avoid crimes if you subscribe to the particular world view that the stronger should be allowed to take whatever they want and that (at least the existing) states, law, etc. are superfluous or illegitimate. Crimes only exist in the presence of law; if you deny law, then the concept of a crime simply does not apply to you.
On the other extreme, some people enjoy a less stressful existence very much and prefer to never take anything by force. For them, following the law (i.e., not doing crimes) is straightforward for the simple reason that if everyone does it, everyone gets to live a stable life.
The real world falls somewhere in the middle - the majority of people seems to be fine with following the law, but some prefer not to; many laws are very accepted and considered "good", some not so much; plenty of people decide that in some cases they can readily break the law (think of speeding), assuming that they can live with the consequences, and so on and forth. Some countries tend to the one side, some to the other. Life is messy.