I struggled with this as well. I don't naturally enjoy creative writing that much and waxing verbose about my emotions and life experiences isn't a strength of mine. I'm more of a technical and matter-of-fact writer. But I struggled through probably a dozen different ideas/drafts of my opening paragraph(s) and solicited a lot of feedback and the end result was something really personal, down-to-earth, and "me". 
The link above (Essay workshop 101) has good examples and ideas. What I did is I went through my entire life from my first memory to now and wrote down (on paper, not just in my head) every event that I, in retrospect, decided had a major impact on me. Some things were "big" (death of a relative) and others were more personal (best friend got in car accident, spent week in PICU when I was in 8th grade--first time I really considered 'mortality of man'). A lot of what I wrote down wasn't even tangentially related to medicine. I ended up with about a dozen events that had in one way or another profoundly moved me. Then with each one I thought of how I could tell that story in a way that would emphasize my interest in medicine and highlight the development of character traits that qualify me. Then I decided which story felt best and ran with it.
That got me a couple of strong opening paragraphs. Then I spent several paragraphs on my major ECs (research, volunteer experience, work in hospital, etc.) and returned to the ideas in my intro in my concluding paragraph.