Utopia/Logical Weirdtopia
There's an infinite number of universes that anyone can teleport between. Thanks to the infinite hotel paradox, each person in each universe find their own personal utopia.
Topological Weirdtopia
We live in a five-dimensional world with a huge curvature. There's billions of people within walking distance. Everyone has a built-in GPS, because otherwise you'd never find your way home.
Even weirder: After we're uploaded, we start just using geometry in games. You get somewhere by willing yourself to be there, and your perception of it doesn't include geometry.
Government Slightly Weirdtopia:
The government is a random sample of the population. I suspect it wouldn't actually be that different, but someone ought to try it.
Government Weirdtopia:
The government is a hive mind. It gives laws using IP over Demographics. People protest against it including the death rate, but it argues that it can't stop that any more than you can stop using certain brain cells.
Economic Weirdtopia:
Money grows on genetically modified spiders, which you have to go around and kill for money. You can buy stuff from other people, in which case they don't have to kill spiders, but mostly you get stuff from NPCs, who just destroy the money. You can also sell stuff to them, in which case they produce money and destroy the item. If you die hunting money spiders, you are reincarnated at the nearest graveyard.
Another:
Everything is free except advertising. You get the money to advertise by putting ads on your products.
Yet Another:
A sort of quantum teleportation of happiness is discovered. It's possible to buy someone else's happiness, and no matter how much you buy, you get the full effect. Billionaires are ecstatic beyond comprehension.
Cognitive Weird... event:
At first luddites choose not to be uploaded, but eventually they're forced to by the eminent domain laws. If they're not going to use that body mass to think, they'd better give it to someone who will.
Cognitive Weirdtopia:
The world is turned into a giant computer that makes the simplest possible extremely happy being. Everyone's extremely happy, but they can't think beyond that.
Another one:
In order to prevent people from modifying themselves so that they can't or don't want to modify themselves back, they're allowed to modify one other person, but not themselves.
Everything is free except advertising. You get the money to advertise by putting ads on your products.
I thought this one up and came to this thread to post it before seeing that you'd already got it.
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...