As I understand the standard picture of modality accepted by contemporary philosophers, there's a space of possible worlds, and this - the actual world - is one of them. It has some special properties, being concrete or realized in a way that the other, merely possible worlds aren't. But this picture seems to run into trouble, for reasons that I've previously mentioned in passing.
In brief: the modal "multiverse" is seen as static and necessary. Contingent facts vary from world to world, but the worlds themselves remain constant, and hence world-indexed facts (e.g. "P is true at w") hold necessarily. But then, if it's a property of our world '@' that it is actual, then it seems that "@ is the actual world" comes out as a necessary truth. We're stuck with narrow fatalism. That's bad. We should be able to make sense of the idea that our world's actuality is a merely contingent fact, and that other possibilities could have been actualized instead. But to achieve this, we must deny that actuality is an intrinsic property of any possible world. That is: there's no red flag built into modal space to specify actuality.
That's not to deny the existence of the actual world, of course. I simply think we should deny that the actual world is a possible world. Instead, I think it is a fundamentally different kind of thing, existing quite separately from modal space. This allows it to have genuine contingency, by escaping the bounds of the static and necessary "modalverse".
We can motivate this idea from another direction too. Possible worlds are typically characterized as "ways a world might be" (see, e.g., Stalnaker). There's a possible world to represent each way, including the way the world actually is. There's a possible world representing that. But the representation is clearly not identical to the thing itself. There's a possible world representing "the way the world is", and then there is the actual world, that concrete thing which contains us - flesh and blood - and not mere abstract representations of "the way we are". As someone (van Inwagen?) noted, we wouldn't dream of identifying "Socrates" with "the way Socrates is". It doesn't even make grammatical sense. So why make the same mistake with the world?
Despite the misleading name, "possible worlds" aren't really worlds. (We're not Lewisian realists here.) They're just abstract representations. Maybe they're primitive entities, or maximal properties or states of affairs, or sets of sentences in an idealized language; the details don't much matter. In any case, the actual world is clearly a very different kind of thing. It really is a world -- a concrete thing, filled with other stuff, real entities, and not mere representations of those entities. Since possible worlds aren't really worlds at all, it follows that the actual world is not numerically identical to any possible world. Rather, it corresponds to that possible world which represents "the way things actually are". There's a representational relation between them, but representation is not identity. (Compare: a photograph doesn't really contain you - the concrete person - as a part. I could cut it up without thereby decapitating you.)
So, I see three major advantages to denying that the actual world is numerically identical to a possible world:
1) Consistency. All possible worlds remain on an ontological par. You don't have one special one made out of concrete stuff while all the others are abstract things. Instead, we can hold that all possible worlds are the same kind of thing, and the actual world is simply a different kind of thing.
2) Grammar. "Ways things are" are distinct from the things themselves.
3) Genuine contingency. We can accept that the "modalverse" is static whilst avoiding fatalism. The actual world is contingent, and can be so because it is outside and separate from the modalverse. No possible world has the property of actuality intrinsically. Instead, it is a relation that holds between the static possible world and the contingent actual world. This makes the relation itself contingent, of course. If the actual world had been different, then it would correspond to a different possible world. None of this requires any change in the modalverse itself. The changes all occur in the fundamentally separate space of concrete actuality.
Update: Ah, it turns out Kripke beat me to it.