Planning what to bring to New Zealand is very much influenced by what it is you'll be doing once here. Nonetheless, first on your list should be a sense of adventure. In this land of adventure sports - bungy jumping, skydiving, white-water rafting and more - you quite simply have to experience thrills in one way or another.
There are no shortage of shopping opportunities in NZ so whether you forget a warm jumper, one of your hiking boots or some pots and pans for that campervan you just might buy whilst here, you'll be able to find a shop selling what you need. On this note, for just about anything you'd need (and especially on a budget), check out The Warehouse. These stores are found in most major towns around New Zealand and are the down-under equivalent of a WalMart.
Even if you don't plan on doing many long-distance hikes while in New Zealand, be sure to bring a good and sturdy pair of walking boots (at the very least, comfortable walking shoes). Outside of the multi-day Great Walks and loads of other backcountry walking opportunities, New Zealand is blessed with dozens and dozens of fantastic short and scenic walks that you won't want to be doing in your finest evening shoes.
Other essentials include a day pack (outside of your main pack or suitcase), swimming suit, rain jacket and warm clothes if you're coming during the colder months of March - October. Even if you're here in the summer months, it can get quite cold during the evenings - especially in the mountains - so warm clothes are suggested. Worst case scenario, you can buy some New Zealand merino wool whilst here.
If you'll be spending a lot of time hiking, you'll want to bring gators to protect your bare legs from speargrass and matagouri bushes whilst in the backcountry. While there isn't an abundance of wildlife in NZ, a pair of binoculars might be a good idea if you'll be spending a lot of time tramping. If you have a good, lightweight tent it would be worth bringing this, although you can always grab one used or cheap here. Similarly, if you'll be camping or tramping, bring a good quality sleeping bag (though these aren't necessary if staying in backpackers as linen is almost always provided). Pack a good Nalgene water bottle or equivalent as you can drink the water from most streams in NZ.
In the toiletries bag, you'll want some high SPF sunscreen as the sun is extremely strong in New Zealand as a result of a hole in the ozone layer. You'll want to lather up even on cloudy days (really). Be sure to include some strong bug spray to protect you from the ubiquitous sandflies found in many parts of the South Island. A small pocket sized torch or headlamp will come in handy when checking out caves or when you've arrived at your backpackers late after a few too many Speights.
Ladies, while there are plenty of backpackers here and New Zealanders in general dress casually, you'll also want something smart for bigger towns and cities or an evening on the town. Considering this, you'll want to bring along one of your favorite dresses. Something that can be worn if you decide to splurge on a nice meal or alternatively to the beach. Guys, a nice pair of jeans will do you just fine. If you'll be working in New Zealand while here, go ahead and bring a pair of black shoes and pants in the event you end up working in the hospitality industry.
Techies will want to have an understanding that the internet is often hard to find here and also unbelievably expensive. Book worms should know that books are also outrageously expensive. Either bring a few you'll be keen to swap, or perhaps now is a time break down and buy a Kindle.