Where are the worlds in many-worlds interpretation? What does it mean in MWI for other universes to exist? Are they in some sector of spacetime beyond our cosmic horizon or is it more complicated? 
I'm not asking this on Philosophy SE because people on there are generally not as acknowledged in physics/mathematics as here and the crucial part of the answer is a good knowledge of MWI itself.
 A: In nonrelativistic quantum mechanics the wavefunction is defined on configuration space.
So for $n$ particles there is a $3n$ dimensional configuration space. And the quantum wavefunction is a function from $\mathbb R^{3n}$ into the complex numbers (or into a joint spin state if you have spin).
There could be regions where the wave is zero or very small, and others where it is comparatively large. Now let's look at what happens when a so called measurement occurs, as an example we will do a Stern-Gerlach device meeting a spin 1/2 particle.
The particle comes in going in the $+\hat y$ direction, say along the $y$ axis. The particle will have some width in the $\pm\hat x$ direction and as it travels in the $+\hat y$ it will widen and split and form two branches, much like the capital letter Y. So over time it starts out having he wavefunction be nonzero near the a horizontal line by the bottom then advances to become nonzero in a horizontal line a bit farther. Like a line of traffic approaching a fork in the road. These are the places in configuration space where the wavefunction is nonzero.
And it really is in configuration space. The wavefunction is not some field in space and time. This means the configuration has many directions $$(x_1,y_1,z_1,x_2,y_2,z_2,\dots x_n,y_n,z_n)$$ and one of them the $y_k$ that corresponds to the $k$-th particle's position along the $y$ axis so the wavefunction could be zero for all configurations except some of the ones there is a range of $y_k$ and a range of $x_k$ that form a part of that Y.
So what happens is waves split. Much like a water wave could break against a rock and become two waves. But this is not yet two worlds. These waves could meet some other rocks (say, some Stern-Gerlach devices oriented in different directions) and end up overlapping. So the waves can still know about the other one.
But the configuration space is large and they can interact with different things. If the left branch had the $x_k$ get close to a $x_i$ for a different particle (and their $y$s and $z$s are close) they could interact. If you draw the wave so you see the nonzero values for that other particle say as having the z axis be $x_i$ then you might see the left branch go up. And similarly the right branch might go up where up is related to the $x_J$ of an even different particle. So it is much like a series of space ships in a thousand dimensional space and making little detours when a location in the large space means two particles are close
 Eventually the two branches have wiggled into slightly different places in the configuration space to the point where it would be hopeless to have them ever cross each again. Either on purpose or on accident.
So it is like you had a single cells organism that divided and then the new cells went off in different direction in a space that was as big as $\mathbb R^{10^{80}}$ and they will just not meet again. These waves that now interact with themselves but not each other. They are the worlds. They are called worlds because they only care about themselves.
Yes, originally it was just a split and they weren't yet different worlds. But there is no moment they became different worlds. It just became practical for each wave to think of itself as the only wave.
So wavefunctions are functions from a very huge dimensional space into the complex numbers, and there is room in there for waves that describe our universe and that as they evolve forward in time, they never interfere with each other. These are the worlds, and they all live in the same place. If you ran them backwards they would interfere, but you don't.
A: 
What does it mean in MWI for other universes to exist? Are they in some sector of spacetime beyond our cosmic horizon or is it more complicated?

The other universes are not in some other place. Rather, physical reality as a whole is the multiverse, a structure that in some approximations looks a bit like a collection of parallel universes, but also has much richer structure. A universe is a structure within the multiverse in which information has been copied. For example, the version of me that is typing this sentence is in the same universe as you because you are able to read this particular version of the sentence. There is some other version of me that has typed a slightly different version of the sentence and there is some other version of you reading that sentence. There is nothing more to being in the same universe than having information about a particular value of some measurable quantity. There is no space external to the whole multiverse where you could say "Oh, the universe in which Alan typed the word chocolate as the tenth word in this sentence is three feet to the left of the universe in which he typed the word "panda" as the tenth word in this sentence." Rather, those universes are different universes because of that difference in the tenth word of that sentence (and other stuff, like differences in my brain that resulted in me typing chocolate instead of panda).
A: As a quantum theorist, this area of physics perfectly intersects my area of knowledge. A simple Google search can lead you to my favourite site for philosophical inquiry.

The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

[Source: http://plato.stanford.edu/entries/qm-manyworlds/]
If this is not of assistance, maybe I can help.
For every decision you make, and that will ever be made, there exists a universe for every possible outcome. These universes exist until the decision has been made. Then all other universes collapse. There now exists only one universe where you made the one decision and that is the universe you live in. If it makes sense, the universes of the many-worlds interpretations exists in our space-time until the decisions have been made. Then the other universes collapse and cease to exist. I hope this helps and please comment with your thoughts.
