American film and stage actor whose performances in classical Hollywood cinema films made him an American cultural icon [Wikipedia].
Maxwell Smart establishes himself as a movie fan through his references to films and stars of the golden era, with Humphrey Bogart being a clear favorite - so much so that when driving through the Bijou Theatre which is on the route that he has selected as the quickest way to get 99 to the maternity hospital. he regrets not being able to stay longer since there is a Humphrey Bogart movie playing there [Episode #119: "And Baby Makes Four"].
This also explains his eagerness for the assignment in the exotic city of Casablanca as it is the setting for a Bogart film of the same name, as well as the fact that he adopts an impression of Bogart's voice and persona while there, and even makes a reference to looking for the Maltese Falcon statuette from another Bogart film [Episode #36: "Casablanca"].
Max imitates Bogart twice more when he finds himself in situations reminiscent of the star's films - while protecting Trinka Markoff from two KAOS agents who resemble characters from the afore-mentioned Maltese Falcon [Episode #65: "Maxwell Smart, Private Eye"], and while searching for hidden treasure a la The Treasure of the Sierra Madre [Episode #117: "The Treasure of C. Errol Madre"].
None of these impressions is explicitly acknowledged in the dialogue. However, on the latter occasion, two of Goldmouth's men pick up Max's hat and appear to think that wearing it makes them look like Bogart who they do mention by name.
A less obvious Bogart reference occurs when Max is activated as an Ensign in the Naval Reserve aboard the USS Yorktown. When he toys with a pair of ball bearings while issuing orders to his men, it is in imitation of Bogart's portrayal of the unstable Captain Queeg in The Caine Mutiny [Episode #98: "Temporarily Out of CONTROL"].