My glib definition of "wealthy" is a person who doesn't need income ever to maintain his lifestyle. Even in Europe, they tax income like us more or less and have a VAT (sales tax) around 20% or so. A billionaire is largely unaffected by either, or can easily dodge taxes on income, as they can here. Sweden has more billionaires per capita than does the US.
I figure once you get to a hundred million or so, you are largely immune from taxes (other than estate taxes, and with a good planned you can largely escape those as well). A liquid net worth of $20 million is ample as well for most folks.