Actually, the greater threat is to New Zealand's wildlife, but they have Customs and Agriculture officers to ensure you're not bringing in invasive species or contaminants. They even check the bottoms of your hiking boots (sometimes requiring you to clean them) upon entry into the country.

• Passport - everyone needs this so this is a no-brainer.
• Comfortable Shoes - much of the country's activities revolve around participating in the great outdoors. This means you'll be doing lots of walking and tramping (hiking). At the very minimum, comfortable walking shoes are a must, but hiking boots are probably better especially if you're going into the bush.
• Hat - even though sunburn isn't normally associated with a place as rainy as New Zealand, don't take for granted the dangers of UV radiation. A hat will at least keep your scalp from getting severely burned (especially since the country isn't all that far from the ozone hole in Antarctica). If you're wearing a broad-rimmed hiking hat, it could also help protect your neck, ears, and face.
• Sunscreen - again, given the sun's harmful UV rays, it's a good idea to protect other exposed parts of your skin from sunburn.
• Sunglasses - prevents cataracts or other harmful effects of prolonged exposure to the sun's ultraviolet rays on your eyes
• Layered Clothing - this means wearing multiple layers of jackets, sweats, or shirts and taking them off/on depending on the conditions. This is very important to be able to adapt to the variable weather and climate in the country. It can easily go from freezing cold to scorching hot and back in a day. This will at least protect you from exposure to hypothermia or even heat stroke.
• Rain Coat - this will keep you and your equipment dry for the most part (with a rain poncho covering the pack in addition to the body). It rains a lot in Aotearoa and this will at least keep you sane under such conditions (not to mention limit your exposure to hypothermia).

Some other things worth bringing to enhance your experience include...

• Hiking Sticks/Trekking Poles - this is useful for longer and more involved tramping excursions (especially multi-day or very long day hikes). They provide you at 1 or 2 extra "legs" to maintain your balance on stream crossings or alleviate shock to your knees if you're carrying a pack
• Lots of Memory or Film or Portable Hard Drive - the first and third items are for digital photographers. In any case, you'll be taking heaps of photos and you'll want to make sure you can bring all your photos home

Perhaps a greater nuissance is theft and break-ins, especially at trailheads or car parks out in nature. To counteract this, pay attention to your surroundings where you're parking your car and leave nothing valuable in the car as you're out and about away from the car.

Finally, nature is inherently dangerous and unforgiving, and since New Zealand is best enjoyed in the outdoors, you need to be cognizant of these dangers. Below is a list of things you need to be aware of to stay safe in the outdoors...

• Getting lost - always stay on the tracks and heed the signs. Bring a topo map as well as a compass with you if you're on a more involved hike where it's easier to lose the track.
• Hypothermia - given the amount of high elevation adventures, the danger is very real. Always pay attention to the weather reports before undertaking any tramp that exposes you to the elements (especially in high elevations). Bring a rain coat to avoid getting wet and losing heat that way.
• Streams and Rivers - while many popular walks have bridges, other more difficult walks involve crossing unbridged streams and rivers. Use your hiking stick to gauge depth and do not cross if it has been flash flooded or you can't see the bottom. Generally waters thigh-deep or higher are very dangerous for crossing.

If you really want to see the country, you've got to give it at least a month. That gives you time to spend a couple of weeks on each island (North and South Islands), which are distinctly different from each other. We spent 4 weeks there and we felt it still wasn't enough time (especially for the South Island). If time wasn't an issue, I think 2 months is good. However, I believe there are not many people that can take that much vacation time at once.

If you're like most Americans and allow only two weeks, it's going to be rushed. Or at least it will be confined to merely a few highlights such as the thermal parks at Rotorua, Auckland, Christchurch, and a brief stint in Queenstown where you can do a long all-day affair to see Milford Sound.