The actual world is a possible world. This is because everything actual is possible.
While it's not uncommon to find this claim, there is excellent reason to consider this an error; it involves an equivocation on what is meant by 'possible world'.
As used in possible worlds semantics, a 'possible world' is basically just a complete totality distinct from other complete totalities of the same kind but able to be related to them in some way. (In the very strictest sense, i.e., the minimal sense needed for it to be used as the basis of a semantics for modal logic, a 'possible world' is just something along the lines of a member of a set, able to be related to other members of the set, that is associated in a model with assignments of truth values to a set of propositions.) There is nothing about this that requires that 'possible worlds' be worlds, despite the name. You can perfectly well make sense of modal logic by taking a 'possible world' to be the actual universe at a time, or a history at a location, or some sort of perspectival or intentional domain, or any number of other things. It's almost irresistible to assume, when you hear 'possible world', that you are automatically talking about worlds, but this is an assumption that should be resisted. We only get worlds if we add new assumptions. So if we are talking 'possible world' in a minimal sense, it has not been established that the actual world is a 'possible world' in the relevant sense, because that requires additional information that's not actually part of the semantics. And for that matter, the basic semantics says nothing at all about the actual world -- we'd have to add actuality in, too.
It is true, of course, that we often talk about alethic modalities on the scale of an entire world, and so you could very well associate 'possible world' in the semantics with the sense of 'way the actual world could be'. In doing so, we've added additional assumptions we might not add in other contexts, but it's perfectly legitimate to do so, as long as different 'ways the actual world could be' have the features that allow them to be represented as potentially inter-relatable elements in a set that can be associated with truth value assignments to a bunch of propositions -- and since we are (ex hypothesi) comparing distinct 'ways the actual world could be' and the natural way to do that is by using propositions, that's not much of a stretch. So let's assume that we have added this optional assumption that a 'possible world' is not a pure logical object, but instead a logical object that represents a 'way the actual world could be'. Can we then say that the actual world is a 'possible world' in this sense?
The answer is No. Since we are taking 'possible world' to be 'way the actual world could be', the claim, "The actual world is a possible world" is equivalent to "The actual world is one of the ways the actual world could be". But this is not true at all. The actual world is not one particular way the actual world could be; the actual world is just the actual world. To put it another way, if we take 'possible world' to mean 'way the actual world could be', we are taking 'possible world' to represent a "slice" of the actual world, not the actual world itself -- all of the 'possible worlds' together represent the one actual world, and a possible world is one slice of that representation. So 'the actual world is a possible world' is not true, however paradoxical that might sound to the ear; the loaf is not a slice, the deck is not a card, the lottery is not a number, actuality itself does not fall into the genus of particular ways of being actual. And note that this is true even if, in fact, everything in the actual world is represented by something in some possible world.
So there are many possible worlds; the actual world is none of them; the whole set of possible worlds represents the one actual world but only in terms of possibility, not actuality. Obviously, the actual world is in some sense possible; but it is not a 'possible world' in the sense relevant to applying possible world semantics to the ways the actual world can be.*
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* I originally owe this point, from a different context, to Richard Chappell.
