A lot of fans of the 1951 film like to play up the notion of Blanche being a variation of Scarlett O'Hara from Gone with the Wind; this is mainly because Vivien Leigh played both roles, as well as the urban legend that Leigh got the part SPECIFICALLY because Elia Kazan wanted to play around with the idea of "What if Scarlett O'Hara Lost Her Mind" as his take on Blanche. Directors of the original play are rather divided on who's right, and it shows in the performances.
Who's the hero; Stanley or Blanche?
Blanche is obviously the protagonist, but seen from one point of view, she does come in to Stella and Stanley's "happily ever after" and mess everything up. People tend to forget that she is, in fact, a guest and therefore, in some instances at least, completely in the wrong.
You could argue that Stanley is almost as insecure as Blanche, deep down inside. He seems sure that Blanche could potentially tear Stella away from him, and when he realizes what he did in a fit of rage, he breaks down in tears and calls her back, quoting from the stage directions, "with heaven-splitting violence". His tough persona is merely a facade to hide his deep insecurities and fears.
Except that he raped her and cruelly destroyed her relationship with Mitch, breaking her, and then giving her a one way ticket back to Laurel where she had been socially ostracized. That level of Kick the Dog cruelty doesn't tend to come from a place of deep insecurity. It tends to come from the firm belief that what you are doing is right and that the person on the receiving end is to blame.
A rather interesting point with this is that NOWHERE in the script does it say that Stanley raped Blanche. It only says that she faints (meaning she wouldn't know what, if anything, happened anyway) and he "carries her to the bed". This means that this scene (and therefore Stanley's character) could be interpreted one of two ways: either the above dotpoint is correct, or Stanley only meant to frighten Blanche or mess with her a little and never intended to, and didn't, do more than that.
Award Snub: Despite being lauded as one of the most powerful performances of all time, Marlon Brando's performance as Stanley was not awarded an Oscar (and the film did sweep the other three acting categories, with Vivien Leigh, Karl Malden, and Kim Hunter all winning in their categories.)
Fridge Brilliance: Why did Stanley serve in the Engineer Corps during World War II instead of a regular combat unit? Well, a common stereotype of Poles is that they're good at mending things, and one of the roles of Army Engineers is to design and construct dams and flood prevention systems to prevent flash floods.
Fridge Horror: Considering that this play was written in the 1940s, it's a very real possibility that Blanche would have been lobotomized after the story's end...
And considering how Tennessee's sister suffered the fate of being taken to a mental institution and was lobotomized, this could be true.
Given the presence of this plot device in some of Williams' other plays (most notably Suddenly, Last Summer), Blanche's eventual lobotomization is a practical certainty.
Jerkass Woobie: Blanche. She's very harsh towards Stanley (who she sees as a 'Polack' and an 'ape'), and she isn't particularly nice in general, but once you find out about her past, it's very hard not to feel sorry for her...
Moral Event Horizon: Stanley's MEH is generally considered to be raping Blanche, but you could also argue that he crosses it when he tells Mitch about Blanche's exploits (thereby ruining their relationship), or when he presents Blanche with his 'birthday present'... a bus ticket back to Laurel.
Cue the beginning of Blanche's auditory hallucinations.
Although one could argue that his sabotage of Mitch and Blanche's relationship was a good thing, given that Blanche had been deceiving and playing Mitch.
Some extra Fridge Horror here: during the Poker night, Stanley loses self-control and ends up hitting Stella. Considering how quickly she forgives him and how calm she is about it, it seems that it's a common occurrence, and studies show that parents who are domestic abusers will have kids that will grow up to be domestic abusers.
The scene leading up to Blanche's rape at the hands of Stanley and the actual implied rape.
Values Dissonance: Blanche herself, who is seen as an Asshole Victim nowadays for manipulating her sister, constantly living in denial even in the face of the truth, an absolute inability to do anything useful, mooching off both Stanley and Mitch, being an ephebophile and getting kicked out of her position as a teacher for it, telling lies to everyone she comes across (and especially her long line of lovers). There was a case where, during a modern revival of the play, people cheered as Blanche was raped.
On the other hand, Blanche is clearly mentally ill and needs legitimate professional help, yet she has the misfortune to live in a time where the only "help" offered to people like her is lobotomy, and her only family in the world is in an abusive marriage with a man who wants to break her into even smaller pieces than she's already in, and send those pieces packing. (And her sister sides with her husband after he rapes her, and sends her to said lobotomy rather than leave him.)
Aside from that, most characters treat her promiscuity as just as bad as, if not worse than, her mental instability. In today post-sexual revolution society, women are not quite as morally condemned for having lots of partners as in her time. ( Although sleeping with an underage student is seen as worse today than back then.)
Values Resonance: One of the many layers of the play is Blanche and Stanley are pretty symbolic of an "Old South vs. New South" dynamic. Blanche was a faded relic of the bygone Antebellum South (she is, after all, played by Scarlett O'Hara herself,) while Stanley was a modern, industrial, blue-collar immigrant, symbolic of where the South was going. An important discussion when the play was written in 1947, since the South was still rebuilding after the war. However, that same "Old Guard vs. New Blood" debate is showing up all over again, with the newest generation of Southerners being much more diverse and progressive, and frequently at odds with the more conservative previous generation, believing that clinging to the Good Old Ways just isn't working anymore.