Flight of the Conchords is a must-see. Not only are their songs hilarious but also they are essentially the ultimate New Zealanders [or Kiwis]. Think of an even nerdier 'Lonely Island.'
The second video was an animated series from NZ called Brotown which is meant to be ok. I haven't seen it though.
Finally, if you're studying the language, the tv series 'Beached Az' is perfect: It's by Australians who basically created a viral video poking fun at the Kiwi accent and it was so popular it got made into a TV series. Below is the video that started it all...
