Too late now, but I wish I could get my medical records all the way back to infancy. I recommend that you request a copy of your record -- while you still can -- every time you stop using a provider.
Many providers keep your records for 10 years or less after your last contact. Most will want to keep your record for at least 3 years (after your age 18 for kids) for potential use in defending a malpractice suit. You can keep your own records indefinitely. You can also review them for errors before passing them on to a new provider.
You cannot actually make a complete "copy" of an electronic (digital) record. You can only see truly complete electronic records on a computer screen using the software that recorded and maintains them. However, you can demand a reasonable facsimile to keep on your own media even if it consists only of computer generated "pages."
Consider maintaining your own patient-centric records in the cloud so you -- and providers to whom you grant access -- can use them in an emergency away from home.
I hope cloud-based electronic record vendors will someday allow patients -- and other providers designated by patients -- direct read-only access to records without going through the provider who created the records. Maybe the patient could even elect, presumably for a fee, to maintain the record indefinitely.