I had my 19w scan last week and found out I've got a low lying placenta (anterior). I read up on it in one of my pregnancy books. Apparently 5% of women have this. Of those, in 95% of cases, the placenta moves up as the belly expands and a vaginal birth is possible. At the moment, my placenta is quite large relative to the uterus.
The book also said there are four grades, and a caesarean is only necessary for grades 3 and 4. Grade 1 - lying near the cervix. Grade 2 - edge of placenta touching the end of the cervix. Grade 3 - partially covering. Grade 4 - completely covering the cervix.
I was also told I may need another scan in my third semester to check its location.