Most embarrassing exam was in high school before going to college. This one I vividly remember even today. The old female doctor I had always had me strip completely when I visited her for any reason. I had a physical every year with her because I wrestled, and last year before going to college I also had to strip naked.
I had several physicals with her, and I remember keeping my briefs on on few occasions even though the nurse told me to "remove everything, including your underpants." The doctor came in and after exchanging hellos and asking me how I felt, she always told me to remove my briefs. So I was always naked in front of her when I was in the exam room. She always did a genital exam, and made sure my foreskin retracted every time. On the very first visit however, she did use an orchidometer during the genital exam. (as I later found out what that instrument was)
After the genital exam, there was a part where she made me walk back and forth in the buff to check the posture. I felt uneasy when I had to walk back and forth for posture check without anything covering me. Then I always had to part my feet and touch my toes briefly as she parted the buttock and did a visual check.
After the posture check, she used to tell me to get dressed, but this time she told me to put my hands and chest on the exam table. She decided to give me a rectal exam since I won't be seeing her anymore, and that she wanted to make sure everything was good before I started wrestling in college. It was brief, but rather uncomfortable and told me to just relax, and that it will be cold.
I did get hard, and I had to lie down on the table afterwards, I was covering myself, but she told me to move my hands as she asked me if it hurt when my penis was "like that." After that I was allowed to get dressed.
She was a very gentle old doctor and seemed to really care about my well being. But I do think that she may have enjoyed giving physical exams to athletic males in the buff.