The eponymous heroine defies summation: it is impossible to assimilate one fixed and definite interpretation of her words and actions. This means that she is a captivating character since the audience is constantly guessing at her 'true' motivations, thus empathizing with Antony's fascination and frustration with her. He veers between calling her "kite" and "boggler" and "the armourer of my heart"; nothing in the play concretely proves whether she is "cunning past man's thought" or motivated by "the finest part of pure love". However, it should be remembered that the play seems to deliberately discourage cut and dried moralistic assumptions - for example, it is impossible to define whether Casear means to treat Cleopatra graciously or rudely, and thus we ultimately have to withhold judgement on him.
Cleopatra was vilified by the Victorians who found her amoral; her vicissitudes were interpreted as signs of instability and her sexual voraciousness was thought improper. A Victorian theatre-goer is rumored to have remarked "How different from the life of our own dear Queen" when leaving the theatre. Her sexual games are shown as threatening Antony's masculinity; remember she "wore his sword Philippan", or assumed the object restricted only to men. She is constantly striking poses and playing games, or pretending to be ill to arouse sympathy, or teasing Antony and insulting him: Cleopatra is the ultimate flirt. However it should not be forgotten that she is past her prime: in anger Antony calls her "half-blasted" ('withered') and she calls herself a "blown rose" (a wilting rose that has already bloomed). Her flirtation comes from experience, not innocence, and is thus all the more threatening.
She also exhibits violent qualities -"I'll unhair thy head!"- which would have been hard for a Victorian audience to stomach. Their favourite Shakespearean heroine was the chaste, constant and selfless Cordelia in King Lear, who is in many ways the antithesis of Cleopatra.
For further reading see:
Dicket, M., Not Wisely But Too Well - outlines traditional condemnation of Cleopatra's behaviour
Paglia, Camille, Sexual Personae - good for putting her violence in context
Stewart, J.I.M., Character and Motive in Shakespeare - defends Cleopatra from charges of inconsistency.