Yes, Bogart's performance is classic, and Peter Lorre and Sydney Greenstreet are terrific -- they usually are. But the film suffers from the production code of the day; Hammett's novel holds up, and the sexual politics of it wasn't allowed to be transferred to the screen (although it could have with better writing -- Casablanca has a lot of dark sex jokes).
The biggest problem with the film is Mary Astor. I don't find her attractive and her performance is mannered and oft putting -- which is a disaster for a femme fatale. In the novel, the character comes across as much prettier and smarter, and the sexual relationship with Spade makes her much more devious; it also makes the love talk at the end and Spade's rejection of Brigid logical. In the film, when this conversation starts, one is left wondering, "What?" These two have barely been on screen together and now there's talk of true love?
One part near the end illustrates the problem with the story as filmed: In the book, when Gutman claims a thousand dollar bill is missing, Spade makes Brigid get naked in the bathroom as he inspects her and her clothes to see if she took it. Brigid protests, but is not modest, and Gutman is surprised that Spade would do this. This scene reinforces Spade's cold demeanor, the sexual relationship between Brigid and Spade, and impresses Gutman with Spade's icy thoroughness. As filmed, Brigid just makes a silent, knowing nod of No, and that's that. The Hayes Code eradicated a key scene, and the writing didn't attempt to find a way to make up for this loss.
If Brigid had been played by a smarter, more seductive actress and the sexual relationship between her and Spade been alluded to, then the dark motivations of the story and Spade's character would be fully realized. As it is, it's a well cast movie (but nearly destroyed by one casting flub, Astor) and influential in terms of character, pace, and camera choices. It may have been the first noir, but that alone doesn't make it a classic. As it is, watching it is more history than enjoyment, while the novel still holds up as well written detective fiction.