So, having watched the Claudette Colbert 1934 version of Cleopatra and the Elizabeth Taylor 1963 version, I saw that TCM was showing the Vivien Leigh 1945 version, so I went ahead and taped it. At first, having listened to the book-on-tape Cleopatra: A Life, I griped about historical inaccuracies, but then I found a source that gave me a quickie biography and realized that, actually, none of the movies were all that fussy about precise historical details.
Each era takes from the story what's important to them. In 1936, Cleopatra was a wily and shrewd manipulator; in 1963, the film focused on Mark Antony's (Richard Burton's) obsessive love for Cleopatra; in 1945, the film focused on Cleopatra's childlike nature (She was after all, 21 years old to Caesar's 52) and Caesar's wise, fatherly affection for her (In reality, she had been the effective ruler of Egypt since the age of 18 and she had a son with Caesar nine months after meeting him) calls to mind the shows Father Knows Best (before my time) and My Three Sons (I remember watching this).
Apparently, there's a Cleopatra film in development today and Angelina Jolie is scheduled to star in it. What would a film about her be like today? My guess is that it would focus on her executive abilities (which were considerable, she'd spend a few hours each morning hearing cases and issuing decisions) and she'd probably be portrayed as quite determined to pursue whatever goal she had in mind that day.