Why don't Vladimir and Estragon leave at the end of Waiting for Godot?
Waiting for Godot is one of the most famous plays in the category called the Theater of the Absurd. Writers whose works fit in this category stress that life has no purpose and the human condition is simply cruel. Vladimir and Estragon do not leave at the end of this play because it reinforces this idea that their existence is meaningless. Everything(one) in the play is counting on the fact that Godot will eventually show up, but by the end of the play, the characters and the audience are left with the hopeless feeling that Godot will never come. Because the name Godot contains the word "God", many critics believe that Beckett was also making the statement that many people put their faith in God but He is never going to show up to really save them.
They can't leave because they are waiting for Godot. That is the limit of their existence, the reason for their being. The only order that exists in their world is their mission to wait for Godot. If they were to leave and Godot arrived, what then?
Someone has created a funny cartoon based on this play in which guinea pigs play the characters. That is a good image for Vladimir and Estragon. It is as if whoever Godot turns out to be is testing them, trying to see if they will wait and how long they will wait. I've pasted the link to that cartoon below.