Atlanta Thrashers
Minnesota Wild (Though the North Stars have)
San Jose Sharks
Phoenix Coyotes (the Winnipeg Jets never made it either, though a really old team called the Victorias did
The Quebec Nordiques also never made the finals until they moved to Colorado.
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Six NHL teams have never made it to the finals, Phoenix Coyotes San Jose Sharks Nashville Predators Atlanta Thrachers Minnesota Wild and Colombus Blue Jackets