That particular haka is called the "Ka Mate," composed around 1820 by Te Rauparaha "as a celebration of life over death." Rights to its use belong to the Ngati Toa tribe, which has agreed to let the All Blacks use it.
Because the All Blacks are the best team in international Rugby, the Ka Mate is the most famous haka, to the extent that some people have a little fun with it. (Controversially, I may add. New Zealanders as a whole take the haka very seriously).
Since 2005, the All Blacks sometimes perform a new haka that was written specifically for them, the Kapa o Pango. It refers to "warriors in black" and "the silver fern," a symbol for New Zealand sports. It includes touching the earth to draw strength from it and a motion to draw strength from the ancestors into the lungs. People who thought this was a "throat-slitting" gesture criticized the All Blacks for it.
Haka are not just for men, though. Here is a haka from a Maori Studies university class. I love the expressions on the women's faces!
Each branch of the NZ Armed Forces, individual units, the police, all have their own hakas. Here is a good one from an army reserve unit.
Here is one for a sad occasion: A member of the 2/1 RNZIR Battalion, killed in Afghanistan, is being honoured with his unit's haka at the funeral.
Finally, the haka is not unique. Many Polynesian islands had similar dances. On the occasion below, before the All Blacks' haka is the Tongan equivalent, the Sipi Tau.
The Samoan dance is below.
Other teams must wish they had something similar. Well, Wales had a pretty good response to the haka in 2008. (Sorry for the poor quality).
The Irish tried something a little different in 1989.
But the best answer of all, in my opinion, was this Scottish ad, doubtless inspired by the film Braveheart.
You know it's not real because not even the Scots would play rugby in kilts!