Americans haven't always paid for health care with public programs like Medicare—or even with private insurance. In fact, Americans used to pay for things like medicine almost entirely out-of-pocket, as seen in this animated graph showing changes in who pays for health care by the California HealthCare Foundation.
Here's are screenshots of 1960 and 2010:
The non-profit CHCF, based in Oakland, California, used data from the Centers for Medicare and Medicaid Services, the Office of Actuary, and National Health Expenditure and made the graphic to accompany its paper Health Care Costs 101.
As you can see, the bright orange bars for "out-of-pocket" costs significantly decreased, with both the red-orange "private insurance" bar and green Medicare and Medicaid bars pushing down other payers. If you go to the graphic itself and press play, you can see the gradual changes from year-to-year in who pays for various health care services.
One thing the graphic can't show visually: The rising overall cost of healthcare. While health care spending was $23.4 billion in 1960, it reached $2186 billion in 2010.
To see the full interactive graphic, go to CHCF.