It is difficult to know what lies around the corner, and illness can not only be sudden and long term, it can be extremely expensive. Medicare supplement insurance is designed for you to pay manageable monthly premiums to protect yourself against unexpected and large medical bills not covered elsewhere. Check to see if it is tax deductible.
A health check is usually required. If you have a family history of a hereditary disease, or live a lifestyle which increases you risk of illness (e.g. smoking), you may not be covered. Certain expensive treatment regimens e.g. antiretroviral therapy, may also be excluded from your policy. If you are really keen to have cover for something, which the insurance company considers a high risk, sometimes they will accept a much higher premium in order to offer you protection. If you are a senior citizen, you could well find that your premiums are quite high reflecting your expected increased need of medical services.