Okay, what do I think I know about New Zealand off the top of my head? Quite a few things as it turns out... I just hope some of them are correct.

I know that NZ is British, and our Queen is the head of state. As she is in Australia and Canada, for that matter.
I know that NZ punches well above its weight in the movie-making and special-effects industry. The Lord of the Rings trilogy was filmed there... and locals did pretty much everything, including making the costumes, weapons, and acting as extras. I watched the extended edition DVDs where they showed how everything was made, and it was incredible what they managed to achieve.
I know that NZ mainly consists of two islands - North Island and South Island. The capital city is Wellington, as I recall, which I think is on North Island? I have some friends who moved there about two years ago.
NZ is also home to the Maori people, who as Polynesians are related to the native people of Hawaii. They have a rich and varied culture which includes some internationally recognisable things such as tattoos (including facial tattoos) and the Haka.
They also don't suck too badly at rugby. I've had the privilege of watching Jonah Lomu on the field; that man's a freight train when he gets going! He was part of the NZ squad that I saw doing the Haka before playing against SA... seeing that performed right in front of you makes your hair stand on end. Especially their facial expressions.

I recall from my schooling in South Africa that name 'New Zealand' comes from the Dutch 'Nieuw Zeeland', which literally means 'New Sea Land'. Yeah, Afrikaners love telling you about all the awesome things the Dutch did.

I know that when travelling, New Zealanders are frequently mistaken for Aussies because of their accent and that this generally annoys them. In the same way as Canadians are frequently mistaken for Americans.

They also sometimes get mistaken for South Africans, because they pronounce the letter 'i' in the same way as we Saffies. That annoys them too.

Karl Urban, who plays Bones in the new Star Trek movies, is a Kiwi. As are a couple of members of Crowded House, I believe? - I seem to recall that the Finn brothers were Kiwis.
Aaand finally... I know I'd like to visit there some day.
How did I do?