Nagg resembles his son Hamm in a number of ways. He's needy and he wants everyone to pay attention to him. He tells jokes that no one listens to. When Hamm abuses him, he sometimes lashes back with a sharp tongue. Nagg is sort of like a retired king who still wants to be in power, but knows that it is out of reach. Instead, he is a minor character in the play. He doesn't get to be the "ham" of the stage. All his whining makes him sound much more like a "nag."
Like Hamm, Nagg sometimes acts very much like a spoiled brat. His neediness is perhaps nowhere as evident as when Nell says that she laughed on Lake Como because she was happy. Nagg is indignant; he wants to be the sole focus of attention. He cries, "It was not, it was not, it was my story and nothing else. Happy! Don't you laugh at it still? Every time I tell it. Happy!" (1.226) Though Nagg is probably the oldest character in the play, he is also the most childlike.
Despite Nell's protests, Nagg does end up going on to finish his joke, indicating something else he has in common with Hamm. Nagg is trying to maintain a sense of humor. He is trying to keep his spirits up. Yet, Nagg himself can't quite push through the story as he intends. (Hamm does the same thing later, when he relates the story of the man and his child.) Nagg says, "I tell this story worse and worse" (1.228). Then he ends up cutting straight to the punch line and skipping half of the joke. At the end, he laughs, but it is "high" and "forced" (1.228). Still, Nagg, for all of his irritating qualities, has not given up.
Nagg is a vulnerable character. He has little sympathy for his son, Hamm, who treats him horribly, but he still cares deeply for his wife, Nell. He wants her to kiss him, he saves her half his biscuit, and later, when she asks why he keeps on telling his joke, he says, "To cheer you up" (1.216). The last time we see Nagg, he knocks on Nell's bin and finds that she is not there. He sinks into his bin and cries.
By contrast, Nagg's relationship with Hamm is marked by cruelty. Hamm derides Nagg for giving birth to him, but Nagg can dish it right back. He tells Hamm that he didn't know that it would be him, suggesting that, if he had known, he might not have allowed him to born (1.526). Yet, in Nagg's last (visible) moment on stage, there is a moment of real honesty between him and his son.
Upon finding out that Hamm promised him a sugarplum, knowing full well that they had run out, Nagg asks Hamm to recall when he was a tiny boy and cried out for his father when he was frightened. Nagg says that they just moved him out of earshot so that he and Nell could sleep in peace. But then Nagg says,
"I hope the day will come when you'll really need to have me listen to you, and need to hear my voice, any voice. Yes, I hope I'll live till then, to hear you calling me like when you were a tiny boy, and were frightened, in the dark, and I was your only hope." (1.561)
Now, in a way, Nagg is still cursing his son and wishing this torment upon him. Yet he is also revealing how much he wants to be needed like he once was. The struggle between Hamm and Nagg is revealed not just as a power struggle, but a struggle of emotional connection. Remember: the world has ended. It's the apocalypse. They are all going to die in this house. Nagg doesn't complain about any of this. His biggest concern is that he is doesn't want to feel so irrelevant and alone.