The fact is, we don't really know, the question is very much up for debate. However one widely accepted theory is that we are in a finite universe with no boundaries. This is a difficult concept to grasp but there's a helpful analogy. Think of a sphere such as a football. The surface area of the sphere is finite as there is only so much material that the ball is made of. But if you placed an ant on the ball it could quite happily walk indefinitely around the circumference without reaching a boundary. If the ant wasn't aware of the 3 dimensional shape of the ball it would say it was in an infinite universe, but of course it isn't.... and can't talk. Our universe can be thought of in a similar way but we have to 'step up' the dimensions. You can think of our universe as the 3D surface of a 4D shape. Now if you're having trouble picturing 4 dimensions, don't worry, no-one really knows what that means unless you consider time which is Einstein's General relativity so I won't go into that here. But as a 3D surface of a 4D object, we can travel in a straight line without reaching a boundary (which is nice because physics doesn't really understand what that boundary could be). This model also avoids an infinite universe which is also nice because physics doesn't like infinites.

Also something to consider when looking up at the stars, if the ant travels in a straight line round the ball, it ends up in it's original position. So it's reasonable that light (travelling in a straight line) from earth could reach round the 3D surface and appear in our own night's sky. Just a shame there's too much other stuff out there in the way.