If you have purchased an iPhone 3G from an approved Vodafone New Zealand retailer, you are able to use a Vodafone Prepay SIM card without any problems, apart from mobile data services (like mobile Internet through the Safari browser).
Why can't I run mobile data services when I have a Prepay SIM with the iPhone 3Gs?
It's because Vodafone have set a special APN intended for use with iPhone 3G plan users (www.iphone-vodafone.net.nz)
How do I change this so that I can run mobile data services with a Prepay SIM?
First, ensure you have the latest update for your iPhone 3G.
To do this, connect your iPhone 3G to your computer, run iTunes, select your iPhone from the list of Devices, and click on "Check for Updates". This process can take a while as the update file is large.
Afterwards, open Settings > General > Network > Cellular Data Network and change the APN field to www.vodafone.net.nz.
The username and password are both blank.