Rugby Union Super 12:
Canterbury Crusaders versus Otago Highlanders; Canterbury Crusaders versus Auckland Blues.
The Crusaders almost always win everything, so it's usually 'envy' rather than 'rivalry'.
Cricket:
Australia versus New Zealand.
The Kiwis are still bitter about that infamous under-arm bowl back in the '70s. Every three or four years we actually win a game against the Aussies, and all the TV sports shows talk about how we're "taking revenge for the greatest act of unsporting behaviour". :rolleyes2
India versus Australia. Two of the best teams in the world; the competition's always fierce when they're going at it.
Formula 1:
Minardi versus everyone else. They just keep trying.