The problem right now is that face time only works on WIFI. The examples they show in the commercials can't be done. I'm not aware of any hospital maternity wards that have WIFI. Facetime might get more popular when and if it ever can be used on 3G.
Guess we're weird...every hospital in our area has free wifi throughout. The first place I ever used an iPhone was a hospital ICU three years ago, after my husband had to be rushed into the ER. No, I wouldn't've used Facetime in that incident. But would it be available? Yes.
I can't see it becoming popular, at least until there are a lot more devices that are capable of using it. Make it compatible with webcams and then you might see more of it in use.