"Nothing is funnier than unhappiness"
Nell makes this statement (in Part two) when she criticizes Nagg for laughing at Hamm's misery. Beckett has called it the most important quote in the play, as it defines the essence of his absurd tragicomedy. Beckett peppers his generally somber, philosophical plays with an astounding amount of low comedy; after seeing one production of Endgame, he was outraged that Clov's pants did not fall all the way down to his ankles at a specific moment. The example says much about Beckett's view of theater. He wants it to be a naked experience that reveals the grotesqueness and comic nature of his characters. Beckett is by no means a make-lemonade-out-of-lemons writer—he does not force comedy onto a tragedy to make it more bearable—but he sees humor wedded to our pathetic nature. Whether it does one any good to see life this way is up to the audience.
"Finished, it's finished, nearly finished, it must be nearly finished Grain upon grain, one by one, and one day, suddenly, there's a heap, a little heap, the impossible heap."
Clov says this in the play's opening words. In his view, the heap is "impossible"; any single grain is not a heap, and a "heap" is just an accumulation of single grains added to each other. The philosophical way of looking at this quandary is that repetitions prohibit meaning from obtaining, since there is never a final product to scrutinize; it is constantly repeating itself. At the end of the play, Hamm applies the image of the grains and a heap to that of individual moments and a single life. Calling an existence a "life," then, is also "impossible," as it is merely a series of repeating moments. Beckett's view of existence as circular, with beginnings and endings fused, supports Clov's argument. Only death can finalize the moments into a life, and this seems to be what all the characters are after—though they also shy away from such finality.
"Look at the world—and look at my TROUSERS."
Nagg says this in the tailor's voice as part of his story about the tailor and the customer (Part two). The story juxtaposes the horror of God's creation, the world, with the beauty of man's creation, the trousers. The earth is given a hard time in Endgame; Hamm frequently says there's no cure for being on it, he compares it to hell, and the landscape is battered, gray, and lifeless. The story is also about delays and repetitions (the tailor keeps putting off the man's order), another major theme of the play. Finally, Nagg switches between four voices in the story (himself, the narration, the tailor, and customer), just as Hamm essentially controls himself and the three other characters in the play. Nagg's acting emphasizes the self-consciousness of Beckett's play, a feature of the experimental Theatre of the Absurd.
"We're not beginning to to mean something?"
Hamm poses this question to Clov, who ridicules him for his naïveté (in Part three). What prevents him from making meaning is that his world is a repetitive one built on cycles. Since any ending is also a beginning, there is never any finality, and conclusive meaning is impossible. The syntax of Hamm's very question exposes this problem; he delays and repeats words as he attempts to finish the sentence. The idea of meaninglessness (itself a somewhat paradoxical combination) was a major emphasis of Existentialist philosophy, from whom the Absurdist playwrights (of whom Beckett was the major figure, though he denied his place in the school) took much of their ideology. The Existentialists believed that the universe was absurd, beyond the limits of human rationality. While many of them prescribed a solution—devote oneself to a meaningful task—Beckett offers little hopeful advice in Endgame and his other works.
"A world where all would be silent and still and each thing in its last place"
Clov explains his desire for order as he tidies up the room (in Part four). Unbeknownst to him (but known by Beckett), a perfectly disordered room would also be "silent and still"; it would have equal distribution of energy and motion would cease. Just as beginnings and endings are the same in Endgame, disorder and order can be viewed as the same thing.