Do we consider the amount of matter in the universe to be "infinite"? Or do we have an idea about "how much" there is?
In essence, the only correct answer is, "We don't know."
This is for several reasons. First of all, we don't truly know the actual extent of the universe. Because we don't know if the universe is negatively, positively, or has a flat curvature. If the universe has a negative, or flat curvature then it is indeed infinite, and Andrews answer would be totally correct. This would also apply to the Level 1 multiverse idea.
However, if the universe has a positive curvature, then it is indeed very finite. As Brightblades mentioned (in his comment to Andrew), there are two very distinct measures. One is the visible universe, which is the universe which we observe. This is limited by the speed of light. Now this is where it gets a little tricky. Although the origin point for the furthest observable point we can see corresponds to roughly the same time that the universe became transparent to light (roughly 377,000 years after the big bang). Thus the furthest light away we see is about 13.7 billion light years away. But wait a minute! That object could conceivably have moved another 13.7 billion light years. So is the extent of the visible universe 13.7 billion light years, or is it 27.4 billion light years? Actually neither! According to astronomers, the answer is 46.5 billion light years! That's because the entirety of space itself is expanding in all directions.
So, what's the answer? We just don't know! Like I said, it all depends on the curvature. Which is why when talking about our universe, most folks limit themselves to the observable universe. And even that number is under a great deal of debate, with answers anywhere from 10^78 to 10^84 equivalent of hydrogen atoms. Yeah, all those zeros makes it rather hard to comprehend anyway!
The general consensus amongst astronomers is that it makes more sense that our universe is open or flat, however it has not been settled to the point that one can actually give that answer just yet. The question bears more investigation.
The Universe is thought to extend forever, and contain a finite average density of matter, so infinity x finite = infinity. The amount of mass in any finite volume, (including, in particular, the finite volume of the visible Universe) is finite, however. This latter point includes even regions of space that contain the singularities that compose the heart of black holes, which are a finite amount of matter in zero space -> finite/0 = infinite density, even with a finite amount of matter/energy.