A big part of my quasi-Freudian take on the horror genre is the assumption that all horror stories reflect anxieties, either societal anxieties or deeply buried anxieties inside the psyche. I see the figure of Anthony representing different anxieties in the different versions, but in all three he is like an evil Bart Simpson (I read online that there is a Simpsons parody of the story, but I have yet to see it).
"It's a Good Life" represents the anxiety of what would happen if we gave over entirely to the rule of our inner id-child and its unadulterated drives and desires. After all, we all have a little bit of Anthony inside of us, wanting to wish people who piss us off into oblivion or into some twisted punishment to satisfy our desire for revenge. But for the normal human being, this desire for revenge is only momentary, kept in check by the other facets of the psyche, namely the ego. However, when the desires and drives of the id are repressed into the subconscious mind for too long without release, they emerge later in other forms (neuroses and dreams). I would also argue that they emerge in fictional stories.
In the original short story by Jerome Bixby, Anthony seems to be the most id-like, ruling all the remaining members of the town with his savage whims. In the television version starring Billy Mumy, I think the filmmakers also infused the story with a political message about succumbing to despotic rule. The character of Dan Hollis gives a speech about standing up to Anthony before Anthony turns him into a gruesome Jack-in-the-box and wishes him into the cornfield. I think this version is infused with a societal anxiety about Cold War fascism, and so Anthony represents both id-gone-wild and a little fascist dictator. In a sense, Dan Hollis' attempt to stand up to Anthony represents standing up against political oppression.
In the Joe Dante cinematic version, Anthony is transformed in some significant ways. In this version, Anthony changes over the course of the story. By the end, he allows himself to be guided by the schoolteacher who visits the house. In this sense, the Dante version is more like a coming-of-age story. Like the movement from childhood to adulthood, Anthony discovers how to control the drives and desires of the Id. In a sense, Anthony begins to form an ego in this version. This Anthony is also the most sadistic, homicidal, and creative out of the various versions (I love the cartoon subtext in Dante's version).
In Ring, the character of Samara also represents a kind of unrepentant, homicidal id. Basically, Samara has been seriously abused — murdered by her own mother and buried deep in a well, which is a wonderful symbol for repression. Samara, like everything that is repressed, doesn't stay repressed. Instead, she bursts forth, unleashing fury and chaos, enacting her revenge against everyone who views the videotape.