Yes, power scaling laws are what are most frequently found in nature. A straight line on a log-log plot produces a power law. The York U Salary plot turns out to be best fit with a negative logarithm.
As for the mechanisms that produce power laws, physicist have proposed many. See this article for a good summary:
For economic applications, I think the most straightforward mechanism is called preferential attachment.
The basic idea is that given the addition of a new piece of `wealth' to the economy, this wealth will `preferentially attach' itself to wealthier individuals. In other words, the probability of an individual gaining this extra piece of `wealth' is proportional to the person's existing income. So basically the rich get richer...
The interest in economic scaling laws dates back to Pareto, but neoclassical economists haven't pursued it much since then.