Theatre of the Absurd -- a rich topic for discussion here.
If you haven't already, please take a look at the wiki entry: Theatre of the Absurd, which expands upon the salient points that David L. has already pointed out.
Also, while considering the O'Neill play, ponder this quote by theatre critic Martin Esslin, who actually coined the term "Theatre of the Absurd":
The theatre of the absurd strives to express its sense of the senselessness of the human condition and the inadequacy of the rational approach by the open abandonment of rational devices and discursive thought.Eugène Ionesco's The Bald Soprano (La Cantatrice Chauve) -- definitely a prime example, along with his Rhinoceros.
You might also wish to explore Jean-Paul Sartre's existentialist influences, especially through his own play, No_Exit Huis Clos (meaning In Camera or "behind closed doors"). Another existentialist influence to consider is Albert Camus.
Finally, don't forget to reflect upon American popular films' influences: