Nihilism and Absurdity are definitely two ways I would describe this play. "Nihil" is literally Latin for "nothing", which is what this play is, and every word of this play is most definitely absurd. From what my understanding of Existentialism is, I don't think it fits in this play very well (so my understanding is probably wrong). I see it in a positive way, I as an individual am the only person who can figure out who I am and why I am here. In finding ourselves and our places in the world we can achieve true happiness. I know this must be wrong because it is far to uplifting and positive for this class. In this sense, Existentialism does not fit in Waiting for Godot. In a way Vladimir and Estragon are waiting for Godot so he can tell them who they are, but they are not doing it on their own.
Nihilism is the belief that nothing we do really matters. We are insignificant organisms that are in existence in this universe for a short period of time. When we go the universe won't miss us, so what we do doesn't matter. Seeing as Estragon and Vladimir literally do nothing for the entire play, it can be said that they believe in Nihilism, but I think they are too simple to think this deep. They do nothing simply because they don't have the motivation to do anything. At the end of Act I and Act II they way "let's go", but they just stand there because it really doesn't matter. They talk about hanging themselves but they don't do anything because it really doesn't matter. Nothing matters.
The Theatre of the Absurd is also in a way the belief that nothing matters. There is no rhyme or reason, things just happen. The play works that same way, nothing seems to happen for a reason because nothing really happens. The entire play is Estragon and Vladimir waiting for Godot. Yes they meet Pozzo (pronounced like Bozzo the clown), Lucky and the Boy, but at the end of the day they are still waiting and talking nonsense. Nothing happens for a reason.