It depends on the type of insurance and the state. Health insurance coverage is required in Massachusetts, for example. Meanwhile, auto insurance is required in many states, but not in New Hampshire. It varies.
Health insurance coverage is mandatory in Massachusetts for anyone over 18 who can find affordable insurance. Those with low income may be eligible for insurance at no cost.
Yes on Individual plans. Employer Groups have guarantees If you're denied as an Individual there may be a State Risk Pool for you http://www.nahu.org/legislative/HRPs/index.cfm