Actually, I wouldn't be surprised if the "surprise twin" stories on this thread all concern multiple (heh heh, see what I did there? Geddit?!) women.
In the words of Dr Elizabeth Bryan (a doctor specialising in twin studies, basically), writing in 1992: "Until about ten years ago it was not unusual for the second baby to be discovered only after the delivery of the first. Since the introduction of routine ultrasound scanning in pregnancy this is now rare and only very occasionally happens if one baby is somehow hidden behind his twin."*
There are many anecdotes of twin pregnancies that were not detected until birth, even when the mother did go for antenatal checks! Emma Mahony, author of Double Trouble: Twins and How to Survive Them and herself a twin, relates that her parents didn't know they were having twins, until the delivery room.
I believe that before scanning, picking up multiple pregnancies was a case of feeling another baby through palpitation, finding the heartbeat, or noticing unusual values on blood tests.
I can anecdotally relate that in the UK, after the scanning-revolution
, it can still be difficult to find a twin that you already know is there. I was hospitalised during the third trimester for complications, and the staff needed to check the heart rate of both babies.
It took 3 midwives, an on-call doctor, and finally a portable ultrasound machine, before they could get a fix on the heartrate of baby 2! And we knew he was there. Indeed, at one point, he kicked the sensor off.
The incidence of twins in the UK has varied between 1 in 80 pregnancies (1940s and 1950s) to 1 in 104 pregnancies (1979) to 1 in 90 pregnancies (1989). Assuming that the figure is not greatly affected by lack of antenatal care, let us say that perhaps 1 in 90 women who refuse or can not access antenatal care could have twins.
Admittedly, if it is down to philosophical opposition to pre-natal care, rather than lack of access, that figure will get cut down, because twin pregnancy is more likely to cause unpleasant symptoms that push you into making appointments with a nice midwife/doctor.
Basically, it's going to happen regularly, if infrequently. And every time, the story will go around.
*Twins, Triplets and More, page 12