It's been two and a half years and our UC baby has still never officially seen a doctor. I had a doctor friend look over him a week or so after his birth (after bible study one day), and that has pretty much been it.
I don't believe in "well-child visits", and so, even with my hospital born babies, they only went to their first two check-ups after their births. Since then, they have each been to the doctor twice - once for my son to get stitches put in and then taken out of his finger when he was one, and once for my daughter when she was seemed to get sick (throwing up for a week straight) every month, and then when I thought her lymph nodes might be too swollen. (Both times, they found nothing was really wrong.)
I was brought up in a "natural" home. My mom did mostly natural remedies and whatnot and didn't take us (or go herself) to the doctor unless absolutely necessary (say, for a refill on asthma medication).
My children have visited the chiropractor far more than any other doctor.

I have quite a few doctors and nurses in my family (and among my friends)... and many of them don't think I'm absolutely nuts (although some do). There really is no sense in taking the kids in for "well child" visits. It is likely a doctor won't notice anything in those visits (although, yes, on rare occasion, one might), but since I spent all my time with them, I most certainly do notice changes in behavior and body- so if there is an issue I cannot take care of on my own, I seek medical help. (Often, with my friends and family- unless they recommend I go in to see a doctor.)
We are a medically hands-off family much like my mother and father were. We rely on natural remedies and healthy foods, exercise, etc - and if we need something above and beyond that, we will seek a doctor's attention.