A little bit different twist than the life insurance take, but consider this hypothetical. Person X is pregnant and gets rear-ended in an accident by Toetfeasor Y. As a result of the accident, Person X has a miscarriage. If a fetus is a person, Person X could bring a wrongful death claim against Tortfeasor Y, which would likely net a judgment in excess of Tortfeasor Y's liability policy, and Person X could then make an underinsured motorist claim under her own policy.
As could be imagined (and as alluded to above), this would have a huge impact on the insurance industry and the premiums we all pay.