Her acting in "A streetcar named Desire" is unsurpassed.
It's a pity that some people today, whilst praising Marlon Brando as Stanley Kowalski, complain about her theatrical acting*. "A streetcar named Desire" is (more or less) a meeting point of 2 periods, 2 styles of acting- theatrical (Vivien Leigh) and natural (Marlon Brando), both performances are divine, and it's only because we now favour natural acting that these people fail to see her brilliance. Hers is the perfect way to portray a woman who chooses magic and rejects realism. She disappears into Blanche DuBois and becomes magnificent in the role, not only depicting the extremely fragile and unstable and moody character, but also conveying all the smallest nuances, as her emotions and expressions change every 2 minutes.
Very few actresses (and actors) can do so**. And that's a wonder.
*: But then Daniel Day-Lewis is now and then accused of overacting. I at 1st intended to call the post "In defence of..." but Vivling doesn't need to be defended. There are things that you see or you don't see, and that's it.
**: Which reminds me that I should watch "Blue jasmine"- Cate Blanchett's 1 of the 3 actresses of today that I call phenomenal (together with Meryl Streep and Marion Cotillard) and her character is said to be a modern-day Blanche DuBois.
Update on 17/4:
Here, another person praised Vivien's portrayal of Blanche DuBois, and did it much much better than I did yesterday: http://fritzlovesoscars.blogspot.no/2012/01/best-actress-1951-vivien-leigh-in.html