Again, I find it's best to go to the experts. Here's what Professor Joseph silk says (I'll post it because it's interesting but this is from 2001 & I think we've solved whether or not our universe is flat or torus shaped by now. I'll search some more later):
ESA: Is the Universe finite or infinite?
We don't know. The expanding Universe theory says that the Universe could expand forever [that corresponds to a 'flat' Universe]. And that is probably the model of the Universe that we feel closest to now. But it could also be finite, because it could be that the Universe has a very large volume now, but finite, and that that volume will increase, so only in the infinite future will it actually be infinite.
ESA: It sounds like a game of words, is it?
No. We do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite. So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat.
ESA: ‘Flat' seems to have a different meaning to non-scientists. By 'flat' we understand to be like a table, which has width. Does the Universe have width?
Flat is just a two-dimensional analogy. What we mean is that the Universe is 'Euclidean', meaning that parallel lines always run parallel, and that the angles of a triangle add up to 180o. Now, the two-dimensional equivalent to that is a plane, an infinite sheet of paper. On the surface of that plane you can draw parallel lines that will never meet. A curved geometry would be a sphere. If you draw parallel lines on a sphere, these lines will meet at a certain point, and if you draw a triangle its angles add up more than 180o. So the surface of the sphere is not flat. It's a finite space but it's not flat, while the surface of a torus is a flat space.