If you do not sign up for Medicare during your Initial Enrollment Period, you may have a penalty added to your Medicare premium. If you are receiving Social Security before age 65, then you will be automatically enrolled in Medicare. If you wait to receive Social Security until after age 65, then you will need to plan on enrolling in Medicare on your own.
Use this flowchart to help determine if/when you should enroll in Medicare, to avoid any late penalties.