The Universe is immense, http://www.youtube.com/watch?v=CEQouX5U0fc&feature=related this video says that the diameter of the universe could possibly be around 92 billion light years. And that might not even be the entire thing because that is only the observable universe, who knows how far the unobserved universe stretches. Just thinking that light, so far considered the fastest thing in the universe, would take 92 billion years to travel across the universe really makes you think about how insignificant and tiny the Earth and humanity is. 100 years on the universal time scale is like a nanosecond in our time scale...
I believe that time and space are both infinite. There is no beginning and there is no end. According to this theory, there is no such thing as present tense. Since time is infinite, you cannot catch up it. Therefore, everything that is happening now has already happened. If you were to travel 50,000 years into the future, you would still be living in the past. As far the universe goes, technically, it is infinite as well. This could just be because it's circular. Like the notion of people believing at one time that the earth was flat and that you could fall off the edge of it. Since the earth is "round," you could say in a sense that it is also infinite. That the earth itself has no beginning and no end. As crazy as it might sound, I suspect that the universe is also round. Theoretically speaking, the idea of reaching the end of the universe and somehow falling off the edge of it is just as ridiculous as the idea of reaching the end of the earth and falling off the edge of it. It's impractical to believe that either could actually happen.
It's not impractical to believe you could reach the edge of the universe, since some people (respected theoretical physicist Stephen Hawking included) estimate the universe to be more saddle-shaped than anything else. In fact a round or spherical-shaped universe isn't even a terribly common theory at all.
Moreover, it has been hypothesized that, with space being curved as it is posited to be, if you were to travel in what, to you anyway, is a straight line across the universe long enough, you'd end up back where you started. But the real mind-blow is when you get into the fringes of theoretical physics. For some real fun, watch this. It's nearly an hour long but really worth the watch.