The American Dream
Summary
The American Dream is the story of... well, it isn't really a story.
At the start, Mommy tells Daddy all about a meaningless and very absurd mix up with hats, and Daddy's impotence is more than implied. Grandma enters laden with boxes and makes generalizations about what people think of old people, while everyone awaits an elusive and late "them", who will supposedly bring satisfaction. Mrs. Barker (them) arrives, but cannot remember why she is there. As Mommy and Daddy try to fetch missing things from missing rooms in the house, Grandma explains to Mrs. Barker that Mommy and Daddy adopted a child before, but when he was curious about his sexuality, and preferred Daddy to Mommy, Mommy mutilated him and murdered him. Then, a visitor shows up at the door (not the 'van man' that Grandma had been threatened with), who Grandma names The American Dream. He is physically beautiful, but completely empty and without feeling - he is the twin of the mutilated son who Mommy and Daddy are named in relation to. Mommy is 'satisfied' with this new American Dream, and begins suggesting that he satisfy her later that night, when Grandma interjects a goodnight, breaking the fourth wall, and speaking to the audience. Its sort of a confused play.

Insights/Themes/Analysis
This is all about the replacement of the original American Dream with consumerism. Grandma's homespun wisdom and frank manner are no longer valued in this society where everything can be manufactured and bought - even children and sexuality. The idea that we can buy satisfaction is prevalent, as well as an emptiness in our new values, as characterized by the American Dream, who is nothing but a pretty face.
Another theme is the castration of America. Daddy's masculinity has been stolen, and Mommy's femininity is equally absent. This desexualization of America is connected to the commercialization of sex. This could be interpreted as a message about how sex is becoming a commodity, and commodities are only a step away from losing all value.  In this universe, sex is not only meaningless, but quite absent. It is replaced by other equally meaningless activities. Here, a child is also a commodity, and thus replaceable.
Edward Albee uses many absurdist elements, but The American Dream is not entirely a part of the Theatre of the Absurd, because is does have a message (other than 'life is absurd'). He shows us the absurd world that our society is moving towards, but uses Grandma as a voice of reason, offering us a choice between a meaningless existence, and the old values. When Grandma speaks directly to the audience, she practically appeals to them "Don't become like Mommy and Daddy". This show parodies everyday behavior to the extreme, in an effort to offend and frighten people away from a meaningless existence.