According to wikipedia, in 2005 the median (not average) annual personal income for those over the age of 18 was $25,149. For those over the age of 25, it was $32,140.
As for taxes, they vary widely based on both income level and place of residence. For federal income tax, the tax rate increases with income. The first $7,550 is taxed at 10%, the next $23,100 is taxed at 15%, etc. all the way up to 35%. There are also a lot of tax credits and deductions that make some or all of your income non-taxable, and which ones apply vary widely from person to person. Many states also have their own income tax, and some towns and cities tax income as well. I don't know what it's like in Germany, but there's no way to look at a number for US income and say, "This is how much they would have to pay in income taxes." You would need to know where they live, and also know their taxable income for each tax in order to determine that. It's a stupid and horribly complicated system, I know.
In addition to income tax, there is also Social Security tax (12.4%, $13,243.20 maximum) and Medicare tax (2.9%). Both of those are half paid by the employer. I should point out that Medicare only covers seniors aged 65 years or older, and usually doesn't cover any of the people paying for it.
The federal government also collects unemployment tax of 1.2% on the first $7,000 of income. Some states collect additional unemployment tax as well. My state charges just over 4% on the first $8,500 for new businesses, and the rate changes depending on the ratio of money paid in to the system versus money taken out by business' ex-employees.
My state also mandates that all non-state employees have disability insurance, and the cost gets taken out of your paycheck. I don't know the rate off-hand but it's not large.
So... At the median income of $32,140, assuming it's all taxable (which it won't be), and assuming they live in Florida or some other place with no state or local income tax, you get:
Income: $32,140.00 ($2,678.33/mo)
Federal Income Tax: $4592.50
State Income Tax: (varies by state, some don't tax income)
Social Security (FICA): 1,992.68
Net Income: $25,088.79 ($2,090.73/mo)
This is without any health coverage. That has to be paid for out of the remaining income, and keep in mind that average incomes and the cost of living varies widely within the US. A quick Google search shows that the cheapest you can rent a studio apartment in Manhattan is $1300, while in my area it may cost half that. Comparing income levels between two places isn't that useful if they have a large difference in the cost of living.
Now, I'm currently looking for health insurance, so I have some rates handy. This is for plans offered by a healthcare co-op that leverages the buying power of a large number of small businesses to negotiate lower rates (much like one of Obama's recent proposals suggested) and is located in the state of New York, which I'm told is rather more restrictive towards insurers. (i.e. It's illegal to deny coverage for pre-existing conditions, among other things.)
For a single person, rates range from $245 to $425 per month. The ones I'm looking at are priced near the middle.
For a family of three or more, it goes from $680 to $1100 per month.
I'm assuming the numbers you gave for Germany are for an individual. If so, that means German public health care costs about the same as the cheapest private plan available to me in the US. (which gives only basic health coverage plus generic-only prescription drug coverage.)