As mentioned above, the majority of Americans who have insurance obtain it through employer-sponsored, or group health insurance plans. The coverage has numerous advantages – among them cost (including the government income tax exemption for health benefits), ease of enrollment, and a wide range of plan options. (In addition to a health insurance plan, employees may have the option to purchase insurance for dental, life, short- and long-term disability.) Read here for more details about group health insurance plans.
There are premium subsidies available in the exchange, but you're not eligible for them if the plan offered by your employer is considered affordable and provides minimum value (this is true for your family members as well, if they have access to your employer-sponsored plan, even if the employer-sponsored plan is only affordable for the employee's portion of the coverage; this is known as the family glitch). Most employer-sponsored plans are affordable and do provide minimum value. So if you're shopping for an individual market plan instead, chances are high that you'll have to pay full price for it, without any subsidies.