[MotherBear]

Oh, and honey, too.

Food
There are many restrictions on bringing food into New Zealand. You may wish to consult the relevant Import Health Standard for the items you wish to bring into the country

If you are carrying food, it must be declared. Some items, such as canned baby foods, are allowed into NZ, but other items may require documentation (such as a Phytosanitary Certificate or permit). These items include:

Meat
Eggs
Specific fresh fruit, vegetable and living plant material
Dairy products
Honey from certain countries
Phytosanitary Certificates are available from relevant Government departments in the country of origin.

More information is available about private consignments of meat products.

Honey and products containing honey
Bringing honey to New Zealand is prohibited. It is an unprocessed product and a
potential carrier of bee diseases. New Zealand has a growing and valuable beekeeping industry, which must be protected. In addition fruit trees, flowers and vegetable crops rely on honeybees for pollination.

NOTE: Honey may be permitted from certain Pacific Island nations with suitable accompanying documentation (contact MAFBNZ Clearance)

From WG's link above.

Quick guide to food imports. It all sounds pretty stringent yet I've heard about many people managing to get a lot of their food items into the country. Just read up about the reasons for not importing and then avoid the sensitive items.