We are interested in anything that can provoke the response: "But that's not really so" — discourse that has been made up at least in part (with whatever intentions).
1. The obvious examples are all the established kinds of fiction. They include literary forms such as novels and short stories, poems and cartoons; dramatic forms such as theatre plays and ballets, operas and musicals, movies, television series', and video games; and pictorial forms such as paintings and photography, and sculpture (perhaps even architecture, as a border case). Part of all fiction is a fictional world of some kind. (That's not all there is to fiction, of course: what it is to be fiction is not exhausted by giving rise to a fictional world. In many cases, that world is not much more than a framework or vehicle for something else which is the proper focus; for instance, a painting might depict a certain scene involving a couple of people, but the whole point may be to make a display of great beauty in the portrayal of the people in the picture. The fantasy world in which they appear is of secondary importance.)
In the kinds of fiction listed so far, fictional worlds are described, depicted or staged in a relatively concrete way. Next, there are more abstract forms of art, which also create, in a sense, their own 'worlds'. Abstract painting comes to mind here, or generally all music which doesn't rely on words or drama (i.e. what is sometimes called 'absolute music'). These worlds are much more strange and interesting: they may still share some very general structures, such as time structure, with the real world, but on the other hand can come to eliminate other aspects completely and so create a purity that just by itself has its own aesthetic quality. (There are none of the familiar physical objects, no artifacts or persons in them; they may consist of highly symbolic or abstract representations, or they may be constructions built mostly for reflection on social or artistic constellations.)
An example for an analysis of the world of sounds which underlies most Western music is the first chapter, on the metaphysics of sound, in Roger Scruton's Aesthetics of Music, from which I've also taken the idea of metaphysical apartness that I've used already several times in my postings here. The qualities of such a hypothetical world of sounds have also been made the basis for philosophical reflection, perhaps most famously by Peter Strawson in the second chapter of his Individuals, where he uses the idea of a world of pure sounds to discuss whether a concept of space is required for the possibility of objectively existing individual items in the world.
2. Closely related to fiction, but with a more practical purpose that influences how they are created, are the various sorts of scenarios used for hypothetical reasoning in situations where trying out things for real, or in all possible combinations, would not be feasible (or practical). Scenario construction goes on when business plans are made, when military operations are planned; generally it's commonly employed in planning activities of all sorts, down to very simple everyday situations. ("This is the last train; what if we miss it?" — "Well, we'd have to find a hotel then.")
Somewhat similar to scenarios, thought experiments are used in science and philosophy to conceptually isolate certain aspects of a theory and test whether the results of that theory would make sense under the conditions in the world of the thought experiment.
An influential recent philosophical thought experiment is Hilary Putnam's 'twin earth' example (follow the link for bibliographic references), with the goal of demonstrating that the meaning of words in a natural language cannot be fully determined by the psychological state of a speaker of that language. The Wikipedia article on thought experiments includes a list of other examples from many areas.
As with fiction, the 'worlds' created when scenarios are built aren't the primary purpose; scenarios are made for a purpose (for 'what-if' exploration, hypothetical reasoning, or conceptual exploration).
3. Fiction and hypothetical scenarios have in common that their character as unreal, as made-up for some purpose (whether it is aesthetic enjoyment or practical exploration of possibilities) is usually known to all involved. It would defeat the purpose of a fictional world or a hypothetical scenario if you hadn't known that it's fictional or hypothetical. (How would you enjoy its aesthetic qualities, or pursue its practical purpose, if you weren't aware of that status?) There is another cluster of forms of unreality where this character isn't known, however. It comprises any sort of (intended or unintended) misinformation: lies, misperception, misremembering, falling for rumours; cases of being deceived (both simple and elaborate deceptions, like those engineered in con tricks, even deep deception such as in Othello); superstition may count among them, illusions, and perhaps as border cases also delusions, such as those caused by mental illness.
Not every kind of false statement generates unreality. (If we'd take the set of all false descriptions, unreality would be a proper subset of it.) In order to be an instance of unreality, it must be taken as a candidate reality, so to speak. Merely false statements (such as, for instance, imprecise answers to questions) may not be able to fulfill this role. There might be a grey zone here, but I think its intuitively clear what this condition means, at least in the paradigm cases.
4. There are two more fields of unreality which both deserve a more extensive exposition of their own; therefore I shall merely list them here without commentary, and defer further discussion to later postings. (I'm aware that these two may be a little harder to recognize as fields of unreality somewhat contiguous to those enumerated above; that's another reason why I think they deserve dedicated introductions of their own. For the moment, you simply have to take them on good faith.) One is that of dreams, which I'd extend to a more broad category including also phantasy and daydreaming. The other encompasses the past and the future: what we can access in memories, history, records, and testimony; and what we find in projections, projects, and predictions.
5. With this, we've walked the main areas into which the terrain of unreality can be divided, by its various forms. In this blog, everything is centered around these, qua being forms of unreality. I've already indicated that its their phenomenology as forms of unreality I'm interested in, where phenomenology is taken in a somewhat relaxed sense. In addition, I will of course explore some theoretical aspects, both of the theory of unreality I'm bringing to bear and from many other theoretical fields from which something can be learned about these instances of unreality.
 Roger Scruton, "Sound", in: The Aesthetics of Music. Oxford: Oxford UP 1997, 1-18.
 Peter F. Strawson, "Sounds", in: Individuals. An Essay in Descriptive Metaphysics. London: Routledge 1996, 59-86.