Although the reader is never privy to the thoughts of Hammett's characters, what might the falcon symbolize to each of them based on their actions?
As far as Spade himself is concerned, the falcon symbolizes the key to the mystery he is trying to solve. He has to understand the meaning of the falcon to some of the other characters in order to be able to understand who killed his partner Miles Archer and who killed Floyd Thursby, and why. Spade remains skeptical about the authenticity of the falcon throughout the novel, and he is not surprised when it turns out to be a fake.
For Brigid O'Shaughnessy the falcon is both a valuable prize and a dangerous burden. As long as she has the statuette, or has access to it, her life is in danger. She wants to get rid of it.
For Joel Cairo the falcon is something he has been employed to retrieve for General Kemidov, from whom it was stolen by Brigid. At least that is what he claims. If he got possession of it he might double-cross Kemidov and possibly try to make a deal with Gutman.
For Gutman the black bird is a priceless treasure he has been pursuing for seventeen years. It has become a quest that gives meaning to his life, and it has a greater value to him than its intrinsic value or its value as an antique.
For Captain Jabobi it is just a package he has promised to deliver to Brigid and may be rewarded with her affection.
It should be noted that in Chapter 11 it appears that Caspar Gutman is the only person who knows the history of the falcon or its potential monetary value. He asks Spade if Brigid or Cairo knows what it is and guesses from Spade's reply that neither of them does. Finally he says:
"Well, sir, it's surprising, but it well may be a fact that neither of them does know exactly what that bird is, and that nobody in all this whole wide sweet world knows what it is, saving and excepting only your humble servant, Caspar Gutman, Esquire."
Later, in Chapter 13, titled "The Emperor's Gift," Gutman will feel compelled to tell Spade everything he knows about the history and value of the Maltese falcon--but there is no indication that Spade ever reveals his knowledge to Brigid or anybody else.