As a physics major, some of the comments in this thread make me cringe.
It is unknown whether the universe is infinite. It could be, but then, it may not be. We only know that what we are able to see of it is finite.
What is being called an expansion is a really funky, non-intuitive thing that is happening. What is happening is that the definition of distance, the metric of the universe, is what is changing, such that distances are measured as being longer as time proceeds forward. Basically, if I pick 2 points and periodically measure the distance between those points, I would find the distance between the points to be increasing. Now, here's the mind blowing part: this occurs WITHOUT the points moving at all. The points are stationary, yet, the distance between them is increasing. Observers at these points would measure red-shifts of the points having a relative velocity away from each other; yet, the points themselves are not moving. What this means is that the universe does not necessarily have to expand into anything in order to get the expansion effect that we observe. This is the counter-intuitive part. Our classical notions of volume, distance, and measurement forces us to think that if something is expanding, then it must be expanding into something. But, because of Special and General Relativity, this need not be the case.
As far as I know, we do not know whether the universe is closed but unbounded(like a sphere), or if it is curved open or flat(thus, potentially infinite in both case). This is because we cannot observe either the mass-energy density or the curvature of the universe with sufficient precision and accuracy such to distinguish the different possibilities.
Another mind-blowing thing is that because the speed of light is fixed and finite, when combined with the uniform expansion of spacetime, we find that we are limited in how far we can see into the universe. There is a causal cut-off beyond which we cannot see because to do so requires that light move faster than the speed of light. At the same time, as time continues forward, that same causal cut-off moves further out, allowing us to see further out into the universe. This causal cut-off makes the question of the universe being infinite or finite even more nebulous. For this reason, it has become customary to consider the universe to be only that which we can observe, and reserving the term cosmos for the greater entirety of existence, including that which lies beyond the causal cut-off.
Does that answer any questions, or cause more confusion?
