Deagonx, there is a bracketed tax rate currently in the US. Basically, the more you make, the more your tax percentage is; so it increases not only just the dollar amount but also the rate as you earn more money. There are currently 6 different tax rate brackets.
At least, that is how it theoretically works. However, there are also a bunch of deductions and exemptions that you can take, and wealthy people are in a better position to take advantage of some of those (for example, there is a mortgage interest and property tax deduction - you don't get either if you don't own your house).
Also, long term capital gains are taxed at only 15%, which is equivalent to the second-lowest income tax bracket (those making $8376-$34000 when single for 2010). So, most wealthy people will earn money in the financial markets, which is largely through capital gains. As long as they hold onto the stocks long enough to make it a long term capital gain, the tax rate is lower than most middle-class tax rates.
So, yes, the wealthy typically would pay more in flat dollar amounts. Percentage-wise, they would appear to be taxed at a higher percent as well, but that can be dramatically lowered depending on the source of income.