While a junior star with the Maple Leaf Athletic Club and later the Edmonton Oil Kings of the WCJHL, Norm Ullman caught the eye of Detroit scout Clarence Mohr. There followed an impressive developmental year with the Edmonton Flyers of the WHL, where he received valuable tutoring from coach Norman "Bud" Poile. In 1955-56, he played his first of 13 seasons for the Detroit Red Wings.
Ullman went on to record 16 20-goal seasons, including 12 in a row from 1957 to 1969. His consistent production was matched by his durability, as he missed only 21 games in a ten-year span. One of his patented moves was to skate across the other team's blue line, delay, pass the puck to his wings and move down the slot for a return pass or rebound. His powerful arm strength and quick anticipation made him one of the game's toughest forecheckers and faceoff men. More often than not, Ullman would go into the corners or along the boards and emerge with the puck.
Ullman led all playoff scorers with 16 points in 1962-63 even though the Red Wings lost out to Toronto. In 1964-65, he led the league with 42 goals and was selected to the NHL First All-Star Team. For a time, he enjoyed playing on a potent line with Gordie Howe and Alex Delvecchio. He also played with Bruce MacGregor and Paul Henderson on the energetic Hummer Line. On April 11, 1965, during the semifinals, Ullman beat Chicago's Glenn Hall twice in five seconds to establish a new NHL record for the fastest two playoff goals. The following season, he helped the Wings reach the finals, where they lost to Montreal. For the second time in his career, Ullman finished at the head of the post-season scoring list. At one point, coach Sid Abel claimed that Ullman was his most valuable performer.
The team needed a shakeup by the late 1960s. Trading Gordie Howe would have started a riot, but management wasn't thrilled when Ullman was elected president of the NHL Players' Association in January 1968. When Frank Mahovlich became available in March, Ullman was the centerpiece of the package sent to the Maple Leafs. The next year, he played chiefly with Paul Henderson and Floyd Smith. He eventually formed a solid forward line with Henderson and Ron Ellis, which became the team's most consistent unit for a number of years. The self-effacing Ullman once scored a hat trick to reach the 350-goal mark for his career, but he had to be reminded of the feat by linemate Henderson, who made him retrieve the puck. Ullman was also largely responsible for making the players' association acceptable in the Toronto dressing room.
The 1969-70 season proved to be very trying as Ullman experienced the worst slump of his career. His linemates also struggled and the Maple Leafs fared poorly in the standings. He regained his form in the early 1970s, but the Ballard era was difficult for the Maple Leafs players. In 1970-71, Ullman did register a personal-best 85 points, but this still placed him 67 points behind scoring champion Phil Esposito. As the decade wore on, the average age of a player decreased, making it difficult for someone like Ullman, in his late 30s, to make an impact. In June 1975, Ullman cleared waivers.
The Edmonton Oilers of the WHA refused to believe that Ullman was washed up and offered him a chance to finish his playing career back home. They had originally selected him in the 1972 General Player Draft and waited patiently for his services. He rewarded their faith with 130 points over two seasons, along with the classy leadership people came to expect. He retired in 1977 after being arguably the most anonymous 490-goal scorer in NHL history. Ullman gained a place in the Hockey Hall of Fame in 1982 and stayed in touch with the game by playing on the Labatt's Original Six Hockey Heroes tour.