Here in South Africa once you find out your pregnant you phone your gynae and book an appointment for anywhere between 8 - 12 weeks (this is all my experience alone)
Then at that check up an ultrasound is normally done. Then another one at between 15-20 weeks then one in the last trimester.
You can ask for more if you want they have no problem with that. Afterall you're paying.
I've had two sofar with my 12week mark being on Wednesday. But that's because of an previous miscarriage. My next one will be at 15 weeks.
Sorry I don't know how it works in all the other countries. But at least I've explained me
EDIT: oops! Forgot to add. I have medical aid. (insurance) without it you would probably get 2 ultrasounds done at 12 and around 20 weeks. Because the government then pays for them.