The cover that made Nancy Keith, Howard Hawks's wife, suggest he cast Lauren Bacall in To Have and Have Not (1944).
Hoagy Carmichael at the piano, while Bacall and Bogart glance at each other across the room, in To Have and Have Not. Howard and Nancy called each other Steve and Slim, which is why Bogart and Bacall call each other that in the film.
The atmosphere is just amazing in the film, as a mood piece it might be Hawks's most successful, although it is not his best film.
Bacall, Bogart and Hawks then worked their magic again in The Big Sleep (1946). As so often with Hawks the plot is treated as unimportant; the chemistry and the interactions between humans are what matters.
Ten years later, after several films, she appeared in Written on the Wind (Douglas Sirk 1956), one of Sirk's most distinguished films. Here is a short scene with Dorothy Malone, they play sisters-in-law.
Yet another 10 years later she was with Paul Newman in Harper (aka The Moving Target Jack Smight 1966), a film that is self-consciously aware of its predecessors, such as The Big Sleep (which was also highly self-conscious, but in a different way).
This clip is from The Walker (Paul Schrader 2007), one of her last films, in which she played against Woody Harrelson.
As a bonus, click on this link and you can see Edward Murrow interviewing Bogie and Betty in their home, in 1954. http://www.cbsnews.com/news/archive-lauren-bacall-and-humphrey-bogart-speak-to-edward-r-murrow/
Now she has died, a few weeks before her 90th birthday. She was wonderful, and never more so as when she sang with Hoagy Carmichael in her very first film. So here is another scene from To Have and Have Not.