We present a new (V, B-V) color-magnitude diagram of the Carina dwarf spheroidal galaxy (dSph) that extends from the tip of the red giant branch (RGB) down to V~25 mag. Data were collected with the Wide Field Imager available at the 2.2 m ESO/MPI telescope and cover an area of ~0.3 deg2 around the center of the galaxy. We confirm the occurrence of a substantial number of old stars with ages around 11 Gyr, together with an intermediate-age population around 5 Gyr. Moreover, we also detected a new, well-defined blue plume of young main-sequence stars with an age, at most, on the order of 1 Gyr. This finding is further supported by the detection of a sizable sample of anomalous Cepheids, whose occurrence can be understood in terms of stars with ages ~0.6 Gyr. The evidence for such a young population appears at odds with current cosmological models, which predict that the most recent star formation episodes in dSph's should have taken place 2-3 Gyr ago. At odds with previous results available in the literature, we found that stars along the RGB of old and intermediate-age stellar populations indicate a mean metallicity roughly equal to Z=0.0004 ([Fe/H]~-1.7) and a small dispersion around this value. This finding is further strengthened by the reduced spread in luminosity of RR Lyrae and horizontal-branch stars in the old stellar population and of the red clump in the intermediate-age group. We find evidence of a smooth spatial distribution of the intermediate-age stellar population (~5 Gyr), which appears more centrally concentrated than the oldest one (~11 Gyr). The radial distribution of the old population appears more clumpy, with a peak off-center by ~2' when compared with the Carina center. Star counts show a well-defined ``shoulder'' in the northeast direction along both the minor and major axes. Current data do not allow us to assess whether this feature is the break in the slope of star-count profiles predicted by Johnston, Sigurdsson, & Hernquist. Based on observations collected at the European Southern Observatory, La Silla, Chile, on Osservatorio Astronomico di Capodimonte guaranteed time.