All three are finalists for other awards: Luongo for the Vezina Trophy as top goalie and for the Lester B. Pearson award as most outstanding player in the eyes of his peers; Brodeur for the Vezina; and Crosby for the Pearson.
The other Pearson finalist is Vincent Lecavalier of the Tampa Bay Lightning.
For the first time since the inception of the NHL awards TV special in 1983, there are more than the traditional three finalists for a league trophy.
There was a third-place tie between 2006 winner Miikka Kiprusoff of the Calgary Flames and Henrik Lundqvist of the New York Rangers in Vezina balloting by the 30 league GMs.
Detroit's Nicklas Lidstrom, a four-time winner, and Anaheim's Chris Pronger and Scott Niedermayer are up for the Norris Trophy as best defenceman.
Evgeni Malkin and Jordan Staal of the Pittsburgh Penguins and Paul Stastny of the Colorado Avalanche are the finalists for the Calder Trophy as rookie of the year.
Coach-of-the-year finalists are 2006 winner Lindy Ruff of the Buffalo Sabres, Pittsburgh's Michel Therrien and Vancouver's Alain Vigneault.
The Lady Byng Trophy for most gentlemanly player will go to Detroit's Pavel Datsyuk, Colorado's Joe Sakic or Tampa Bay's Martin St. Louis.
The Frank J. Selke Trophy for best defensive forward will go to Carolina's 2006 winner Rod Brind'Amour, Anaheim's Samuel Pahlsson or New Jersey's Jay Pandolfo.
The winners will be announced June 14 during the televised awards special in Toronto.