Paul Graham — who describes himself as a "manufacturer of economic inequality" — has a really nifty essay on the topic. Some highlights:
The most common mistake people make about economic inequality is to treat it as a single phenomenon. The most naive version of which is the one based on the pie fallacy: that the rich get rich by taking money from the poor.
Usually this is an assumption people start from rather than a conclusion they arrive at by examining the evidence....
If you want to understand change in economic inequality, you should ask what those people would have done when it was different. This is one way I know the rich aren't all getting richer simply from some sinister new system for transferring wealth to them from everyone else. When you use the would-have method with startup founders, you find what most would have done back in 1960, when economic inequality was lower, was to join big companies or become professors. Before Mark Zuckerberg started Facebook, his default expectation was that he'd end up working at Microsoft. The reason he and most other startup founders are richer than they would have been in the mid 20th century is not because of some right turn the country took during the Reagan administration, but because progress in technology has made it much easier to start a new company that grows fast.
...
As a manufacturer of economic inequality, the underlying causes are something I know about. Yes, there are a lot of people who get rich through rent-seeking of various forms, and a lot who get rich by playing games that though not crooked are zero-sum. But there are also a significant number who get rich by creating wealth.
...You can't prevent great variations in wealth without preventing people from getting rich, and you can't do that without preventing them from starting startups.
So let's be clear about that. Eliminating great variations in wealth would mean eliminating startups. Are you sure, hunters, that you want to shoot this particular animal? It would only mean you eliminated startups in your own country. Ambitious people already move halfway around the world to further their careers, and startups can operate from anywhere nowadays. So if you made it impossible to get rich by creating wealth in your country, the ambitious people in your country would just leave and do it somewhere else.