At the moment there are 16 domain name extensions available in New Zealand.

.nz

the latest domain name extension – the shorter version of .co.nz
134,154 active domains

.co.nz

commercial – the mostly used but officially meant for commercial organisations
506,565 active domains

.net.nz

officially meant for organisations directly related to the NZ Internet but nowadays a good second choice when the .co.nz extension is already taken
23,458 active domains

.org.nz

not-for-profit organisations
27,533 active domains

.kiwi.nz

more ‘funky’ alternative for the .co.nz extension. Although there is a .kiwi (without the .nz) extension as well.
4,450 active domains

.school.nz

schools – primary, secondary and pre-schools and related organisations
3,620 active domains

.ac.nz

academic – tertiary educational institutions and related organisations
2,353 active domains

.gen.nz

general – individuals/organisations not covered elsewhere
1,060 active domains

.geek.nz

geeks – computer freaks
944 active domains

.govt.nz

government – national, regional and local government organisations. A moderated domain name.
1,057 active domains

.maori.nz

Māori people, groups, and organisations
881 active domains

.health.nz

registered practitioners and organisations providing health and disability services
256 active domains

.iwi.nz

traditional Māori tribe. A moderated domain name.
105 active domains

.mil.nz

military organisations of the NZ Government. A moderated domain name.
34 active domains

.cri.nz

Crown Research Institutes. A moderated domain name.
7 active domains

.parliament.nz

agencies and individuals who are part of the parliamentary system. A moderated domain name.
11 active domains

Five domain name extensions are moderated (restricted): .cri.nz, .govt.nz, .iwi.nz, .mil.nz and .parliament.nz meaning that applicants need to meet specific additional criteria before they can be registered.

Active domain counts as per March 2018 (source dnc)