What I want to hear about is the 7 lbs.-7 oz. kid who was born at 7:07 a.m. on 7/7/07. Any leads? She will probably grow up to be a poker champ.
I wonder if there are any. You'd expect 11,000/1440 = 7.5 babies to be born in that minute, and 7.5 in the corresponding p.m. minute, for a total of fifteen. About two percent of babies weigh between 7 lbs, 6.5 oz and 7 lbs, 7.5 oz at birth; I'm getting this from this analysis of Norwegian birth weights which is all I could find quickly. (Seven percent of babies weigh between 3350 grams and 3450 grams at birth; one ounce is very nearly two-sevenths of one hundred grams.) So the expected number of 7 lb, 7 oz. babies born at 7:07 (a.m. or p.m., local time) on 7/7/07 is about two percent of fifteen, or 0.3. I'd guess that the number of babies born during any minute is Poisson-distributed; the probability there are no such babies is thus e-0.3, or about 74%.
Then again, as has been pointed out, if you had a seven-pound, six-ounce baby born at 7:08, maybe you'd make everything be 7s just for the hell of it. Hospital staff aren't above this sort of thing. I was born prematurely and weighed five pounds, eight ounces at birth, but lost weight once I was born; the hospital had a rule that babies under five pounds couldn't leave. On Christmas Eve I weighed a bit under five pounds; apparently the records show five pounds exactly, because the nurse felt that I should be home for Christmas. (Given who gets stuck with working at a hospital on Christmas Day, this might have even made sense from a medical point of view.)
Of course, the U.S. isn't the entire world. We're about one-twentieth of the world's population; very crudely just multiplying that 0.3 by twenty gives six. (This of course doesn't take into account the different birth rates or distributions of birth weights in different countries.) Then the probability that there are no such babies is about e-6, or one in 400 (by the way, knowing e3 is very nearly 20 is useful), and even without rounding there probably do exist such supremely "lucky" babies.