The only visa exempt country is Australia and its citizens can travel to New Zealand without a visa for short term stays. Australian foreign residents, however, do need to obtain the new electronic travel authority, NZ eTA (but not to pay the associated tourist levy), regardless of their nationality.
Citizens of 60 countries are now required to obtain a New Zealand eTA. This travel authorization is obligatory from October 1st, 2019.
Can you enter New Zealand without a visa?
Citizens of 60 countries can travel to New Zealand without a visa, but must apply online for the new electronic travel authority: the New Zealand eTA. Pre-registering an eTA application online is obligatory for these citizens from October 1st, 2019. The online form is already available.
Australian nationals are the only exception, since they are permitted visa-exempt travel to New Zealand. However, Australian permanent residents of other nationalities —whether they are from an eligible country or not— will also be required to apply for the eTA (although they are not required to pay the associated International Visitor Conservation and Tourism Levy.)