Sure, I'll play.
Economic: Human desires don't keep up with available resources; the resulting global resource surplus makes efficient resource distribution entirely moot. A vastly (though not quite Vastly) inefficient system emerges which is nevertheless able to maintain everyone in whatever standard of living they choose.
Sexual: Sexual mores vary radically from one community to another. In the absence of resource competition, some subcultures have adopted sexual pleasure -- artificially induced and, by convention, solely induced by others -- as their preferred unit of currency, providing individuals with mechanisms of mutual influence and interdependence... in other words, everyone is a whore. Others have (d)evolved into orgasmium. Others have worked out less overwhelming arrangements. More generally, Rule 34 applies on a vast scale: if you can think of it, there's a community out there somewhere doing it. Mutual disapproval is widespread.
Governmental: There is no single government. In the absence of the need for efficiency, humanity fragments into billions of independent subcultures defined by different strategies for making group decisions. (Many of these are more like large families than anything we would consider governments.) Without any real benefit to either warfare or trade, their interactions are mostly social -- more like forums on the Internet than what we would think of as governments. Obnoxious subcultures are isolated by the collective effort of their neighbors.
Technological: Technology as we think about it mostly doesn't exist. Instead, fully general nanotech packages that extract energy from the Source are integrated with almost everyone's bodies, responding to their thoughts. This is not considered separate from individuals any more than most people today consider their physiology separate from them; mostly, people think of themselves as living simple, uncomplicated lives under their nanotechnologically assembled fig trees, with none to make them afraid. (There are a few subcultures that insist on externalizing technology like spaceships, computers, replicators, houses, supercolliders and so forth; such technophiles, or "tech geeks," are condescendingly tolerated by the majority.)
Cognitive: Some subcultures we would think of as a single cognitive entity... a "groupmind," if you like... while others we would recognize as more normal social structures including distinct individuals. Subcultures of the first type consider those of the second type to be suffering a kind of dissociative identity disorder, and often offer therapeutic interventions, which type 2 subcultures respond to in various different ways. (This sometimes results in cultures being obnoxious; see Governmental above.) The distinction between "natural" and "artificial" cognitive entities is mostly meaningless; individuals (including city-sized ones) consider optimization technology part of their cognition in the same way that we consider families and writing and communities and so forth part of our own.
Utopia and Dystopia have something in common: they both confirm the moral sensibilities you started with. Whether the world is a libertarian utopia of the non-initiation of violence and everyone free to start their own business, or a hellish dystopia of government regulation and intrusion—you might like to find yourself in the first, and hate to find yourself in the second; but either way you nod and say, "Guess I was right all along."
So as an exercise in creativity, try writing them down side by side: Utopia, Dystopia, and Weirdtopia. The zig, the zag and the zog.
I'll start off with a worked example for public understanding of science:
Disclaimer 1: Not every sensibility we have is necessarily wrong. Originality is a goal of literature, not science; sometimes it's better to be right than to be new. But there are also such things as cached thoughts. At least in my own case, it turned out that trying to invent a world that went outside my pre-existing sensibilities, did me a world of good.
Disclaimer 2: This method is not universal: Not all interesting ideas fit this mold, and not all ideas that fit this mold are good ones. Still, it seems like an interesting technique.
If you're trying to write science fiction (where originality is a legitimate goal), then you can write down anything nonobvious for Weirdtopia, and you're done.
If you're trying to do Fun Theory, you have to come up with a Weirdtopia that's at least arguably-better than Utopia. This is harder but also directs you to more interesting regions of the answer space.
If you can make all your answers coherent with each other, you'll have quite a story setting on your hands. (Hope you know how to handle characterization, dialogue, description, conflict, and all that other stuff.)
Here's some partially completed challenges, where I wrote down a Utopia and a Dystopia (according to the moral sensibilities I started with before I did this exercise), but inventing a (better) Weirdtopia is left to the reader.
Economic...
Sexual...
Governmental...
Technological...
Cognitive...