I pulled the data on 'health care' and 'health insurance' off the consumer expenditure pages from BLS. They have info going from 1984 to 2007. Here is a graph of the amounts spent by average consumers in those time periods:

A 4-6% annual increase is a bit more than inflation as a whole. But an interesting thing happens when you compare health insurance and health care cost spending to our income. From 1984 to 2007 total the after tax income went up from $21,237 to $60,858. Thats an annual growth rate of 4.7%. Before tax income went from $23,464 to $63,091 for a 4.4% annual increase. Increases in income outpaced increases in health care spending from 1984 to 2007.
So while health costs have gone up and up and up our income has actually outpaced the increase in health costs. In fact in 1984 our total health care spending was $1,049 on average and our income after tax was $21,237. That means we spent 4.94% of our after tax income on health care. In 2007 the spending increased to $2,853 and income increased to $60,858. That represented 4.69% of our income. While health care costs appear to have gone through the roof, the % of our income we spend on health care actually went DOWN a fraction of a percent.
I should make a couple points about this. First of all I'm looking at average figures. This doesn't really show much of a picture. It also doesn't capture the impact from more and more Americans who are going without health insurance altogether. They are spending less because they are choosing not to spend anything on insurance at all. While we are spending about the same total on health care fewer people are actually covered by insurance. So there is a net loss.
[edit 5/20 : fixed typo in post title]