St. Louis Blues
Another 1967-68 expansion franchise along with the Kings, the Blues reached the Stanley Cup Final in each of their first three years, largely because league rules mandated that the six new teams be placed in the West Division, which sent its champion against the best of the Original Six teams that made up the East. Good luck. (The Blues were swept each time.) Since then, the closest they've come is falling one round short of the final in 1972, '86, and 2001.