Will my medical records be always safe with the doctor?

Generally yes: All medical facilities, including doctor's offices, have a responsibility to keep all health records secure and private. Guidelines for this are spelled out by the federal government under the hipaa rules. Feel free to ask how your doctor how the comply with these rules.

Yes: That is his/her sacred duty.

Define safe ??: In my state, as a pediatrician,I am required to keep records until the kid turns 21 and I haven't seen them in at least 7 years. After retiring a doc must keep the medical board informed of the address where these can be found if someone needs them. When they go past dates,we are required to use a method of destruction that prevents any private info from getting out.