When we would be able to tell with surety that universe is finite or infinite? How can we exactly determine the density of the universe so, that we compare it with critical density, in order to determine its geometry? Does the infinite Universe entails infinite black holes or infinite stars?
The relative recent WMAP result shows, the Universe seems infinite.
However, the "is the Universe infinite" question has a hidden problem: it doesn't matter, how far away can we see, we can't be sure, if anything out of it is finite or not. :-) Thus, it is about a definitely unknowable thing.
The WMAP measured essentially the curvature of the Universe and it found a zero curvature (i.e. it seems to be planar). If there is a minimal curvature, below a measurement precision, and we have a cyclic, spherical geometry, then its radius must be at least 300billion light years.