The question is natural, but I think there is a bit more that we already 'know' (well, we concluded with some confidence) to answer this question.<p>(a) Just because you might be able to move in one direction forever, does not mean the space you're in is infinite. You may imagine the universe as the skin, the surface of a balloon that is expanding: the surface is finite, but still you can move in one direction on the surface forever -- you will wrap around at some point (if you're fast enough to overcome the expansion speed). Now imagine this as a 3D surface of space on a higher dimension balloon for the universe. This is quite a plausible way of imagining this intuitively (as long as you don't ask questions about the balloon space), particularly because it also makes futile the question whether we are close to the edge or close to the center, which bugged me for a while -- we are somewhere on the surface of that imagined balloon, and there might not be a center or an edge, despite being finite.<p>(b) The universe is expanding. In fact, it has expanded already so much that it is far larger than its age, so to say: it's 13.7Gy old, but 45Gly (IIRC) across, most likely. The universe is so large, that light that starts at the farthest spots now will never reach the Earth, because the universe expands that light away from us, so even with the best sensors and a very long time to wait, we will never see from Earth light and thus images from what is far away now. We are quite lucky, though: the oldest light that reaches us now is from the beginning of the big bang (photons started their 'normal' way of travel ~400ky after the BB, and that's what we can actually see!), so theoretically, we do see now every part of the universe at some point in the past (well, unless something obscures our view, and obviously in non-optimal resolution). But this view will fade away, and new light from those farthest places will not reach us in the future anymore (a couple of Gy from now) -- it will be getting darker and darker for us. The farthest places are already completely out of reach, we can only see their past and we will never be able to go there -- a bit like the inside of a black hole is out of reach, but, well, with the boundary around us.<p>(c) When moving at the speed of light, you will never ever reach the spot again that you started at, even with a wrap-around in the balloon model, because the expansion is going on, and even speeding up, so the speed of light is just too slow to keep up with the expansion.<p>(d) Practically, it is of course completely impossible to reach speeds close to the speed of light, for various reasons, e.g., energy needed and harmless cosmic rays becoming gamma rays, etc.etc. Different story entirely. It is good that we have stories to imagine this without the practical restrictions.<p>So the whole question is kinda futile. But interesting. The universe is incomprehensibly huge.