What are the origins of health insurance?

In 1850, the first U.S. insurance firm was founded. It offered insurance against injuries received during an accident. Hospital and medical expense insurance wasn’t introduced until the 1920s. Individual hospitals (and in 1929, employers) offered pre-paid plans to help cover the cost of medical expenses. Employer- (or union) sponsored health insurance became commonplace after World War II when it was offered as a benefit to compensate for limited wages, or as a recruiting tool in job categories with high demand and limited supply. President Truman began throwing around the idea of a government-sponsored health plan during this post-war period. However, it wasn’t until 1965 that Lyndon Johnson signed Medicare and Medicaid into law. In the 1970s, changes in the law allowed managed care through HMOs. Today, as you well know, the options for healthcare plans are extensive and quite complicated.

The earliest form of health insurance (as opposed to life insurance) was "accident" insurance, which typically paid a specific, pre-determined amount to the policyholder if an accident occurred. This was the sole type of insurance available in the United States until the mid-1800s.
The true precursor to modern health insurance began in Texas in 1929. Justin Kimball created Blue Cross to allow teachers in Dallas to pay a hospital 50 cents a month and not be charged when, later, they went to that hospital to have children. This was actually pre-payment and not insurance, although some of them probably never had children.
That hospital maternity plan evolved to include sickness and injury care as it does today. It still covered only the hospital charges. Then Blue Shield was created to cover the growing expense of physician care.