The current, widely accepted model for cosmology is $\lambda$-CDM. The universe appears (exactly) flat, and for simplicity the universe is infinite. Note that we distinguish between the observable universe (which is the local patch that light could have travelled between since the Big Bang) and the totality — we have constraints that even if the universe is not infinite, its size is many orders of magnitude larger than the observable one.
In the literature (especially the popular science one) the details are very muddled, because the consensus around $\lambda$-CDM model is quite recent — relying heavily on detailed measurements of the cosmological microwave background radiation, largely done by WMAP in the last 8 years or so. In a sense, the lay reader should be exceedingly careful when she reads statements (even from heavy-weight scientists) regarding cosmology — it is (perhaps ironically) a fast moving field.
