Medicare Supplement - also called "Medigap" - Insurance
You'll get Medicare Part A (hosptial) coverage when you turn 65. You can elect to enroll in Part B (medical) coverage and pay a monthly premium for it. The monthly premium starts at about $105 per month and can be higher based on income and assets.
If you have both Medicare A and B, you can enroll in a Medicare Supplement plan. Most people choose Plan F, which covers what Medicare doesn't pay for approved services. You can see any doctor you want, nationwide.