Careful too, because excessive scanning isn't good for the baby.
I believe there's no scientific proof but it's useful for people to believe this when scans need to be rationed due to systemic shortages in funding or staff. E.g. In central Europe, it's unheard of to actually require a referral for a scan 
. All hospitals & clinics offer unlimited internal & external ultrasounds for every patient if needed (check-ups, bleeding, reduced movement, any other concern).
Regarding 3D/4D ultrasounds, I had those regularly throughout pregnancy as it was part of the standard equipment however out of 5-6 scans, only one turned out well. It was definitely worth it to see your baby's face earlier...still love looking at the picture! Though the result depends hugely on whether s/he cooperates. I have a super active baby so my main memory was the doctor trying to hold the 4D scanner still for 5 seconds, feeling the baby move during that time, and then you get a distorted nightmare fuel image on the screen :P.
I decided against booking a private session just for pictures since I realised it was too hit & miss. The best picture I got was from my 20wk organ screening, however they generally tell you that 30wks upwards is best since the baby has less room to move around. So I eagerly awaited my 32 wk scan but ended up with nothing at all because her face was bunched up in a corner with loads of umbilical cord in front of it =_=
However, if anyone is still early enough, a 4D/3D scan at 12 weeks is adorable! At that age you obviously can't see facial features but you do see a tiny human with arms and legs happily bobbing around like a gummy bear. That was the only appointment I missed with the 4D machine, but a friend got one done and the picture is amazing.