Medicare Part A

Prior to reaching 65:

Your automatic enrollment in Part A (Hospital Insurance) and Part B (Medical Insurance) of Social Security (or the Railroad Retirement Board) upon reaching 65 years old is contingent upon your application being submitted at least four months prior to your 65th birthday.
You will still have to make critical choices regarding your insurance, such as whether to add prescription coverage.
You will need to enroll in Medicare if you wish to receive coverage when you turn 65 but do not intend to take retirement benefits at that time.

Following your 65th birthday:

When the time comes for you to enroll in Medicare, you'll need to get in touch with Social Security. 

Depending on your work situation and if you have health coverage through your employer, you may want to wait to sign up for Medicare.