From a scientifically-informed netfriend:

If there is sufficient matter in the universe, the universe could be bound but without an edge and without a centre. This might sound strange. Imagine, as an analogy, instead of our intuitive 3D world, a two dimensional world. Imagine flatland creatures living in this world. Now imagine if, that through an axis unfamiliar to them, this surface curved to form the surface of a sphere. The creatures could move forever on that surface and never find an edge. If they traveled in a straight line, they would eventually come back to the point they left. There would be no centre on that surface (their world).

Now extrapolate that by one dimension to consider our world. Just say our universe were sufficiently curved around on itself. If we traveled far enough into space, we would arrive back at where we started. We would not find an edge and there would be no centre.

It has been well established, through general relativity, that matter curves space, into what gets referred to as a 4th dimension. This is not something we can empirically contemplate. The only question is whether there is sufficient matter in the universe. Personally I find this model less weird than a universe that goes on forever or one that has an edge.