Currently, the most popular theory about the universe is that it is bounded, but in more than three dimensions. What this means is that the universe is unbounded to us (ie, you can never reach the edge) but it is not infinite.

To put it another way, the Earth is bounded in 3 dimensions, but unbounded in 2. So if you only ever travel left and right, forwards and backwards you'll never reach the edge. But if you travel in the third dimension, up and down, you can get off the planet.

Likewise, the universe is unbounded in 3 dimensions, but bounded in (probably) 4 dimensions. If all you do is travel up and down, left and right, forwards and backwards, you'll never reach the end of it. But (here's where my understanding gets a little shaky) if you travel in the fourth dimension, time, you can reach the edge of the universe. Or that's what I was taught. This all falls under Einstein's Theory of Relativity.