It struck me the other day that the one thing we found difficult to understand about NZ was the healthcare system, how useful it would've been to have had a really good guide on how to access it properly.
For instance, my son had an injury at school not long after we arrived on the North Shore, rather than take him to casualty at the hospital (which would have been free I found out later) I took him up to a private provider "Shore Care" on the advice of the school. No waiting to be seen, he received excellent care and was stitched up for $40.
In the UK the first port of call for any medical issue is your GP but it can be different here: the GP can be circumvented in some cases. eg. A family member injured their knee ice skating and limped off to the doctors who advised physio treatment under ACC (again at ShoreCare) had 5 sessions free with no months long waiting list either! The physio said next time you get an injury just come here, there's no need to go to your doctor.
If you have health care insurance and want a 'suspect' mole removed you can go straight to a private clinic and get it done, the insurer pays them direct and again there is no need to go via the GP - unless you want him/her to recommend a surgeon to you or don't have insurance.
I never had to use an ambulance, a service that is operated by St John's Ambulance,
and I think there is a charge for it if you do. Some people take out small policy to cover this.
Now don't take this as being the case for all parts of NZ, it could be different elsewhere.
Health Insurance can be organised through a company such as Southern Cross or you could look at an "Expat" type policy from a provider in your home country.
Just found this useful tool on the main forum http://www.moh.govt.nz/eligibility.