We present new BV time series data of the Carina dwarf spheroidal galaxy (dSph). Current data cover an area of ~0.3 deg2 around the center of the galaxy and allow us to identify 92 variables. Among them 75 are RR Lyrae stars, 15 are bona fide anomalous Cepheids, one might be a Galactic field RR Lyrae star, and one is located along the Carina red giant branch. Expanding upon the seminal photographic investigation by Saha, Monet, & Seitzer we supply, for the first time, accurate estimates of their pulsation parameters (periods, amplitudes, mean magnitudes, and colors) on the basis of CCD photometry. Approximately 50% of both RR Lyrae stars and anomalous Cepheids are new identifications. Among the RR Lyrae sample, six objects are new candidate double-mode (RRd) variables. On the basis of their pulsation properties we estimate that two variables (V158, V182) are about 50% more massive than typical RR Lyrae stars, while the bulk of the anomalous Cepheids are roughly a factor of 2 more massive than fundamental-mode (RRab) RR Lyrae stars. This finding supports the evidence that these objects are intermediate-mass stars during central He-burning phases. We adopted three different approaches to estimate the Carina distance modulus, namely, the first-overtone blue edge method, the period-luminosity-amplitude relation, and the period-luminosity-color relation. We found DM=20.19+/-0.12, a result that agrees quite well with similar estimates based on different distance indicators. The data for Carina, together with data available in the literature, strongly support the conclusion that dSph's can barely be classified into the classical Oosterhoff dichotomy. The mean period of RRab's in Carina resembles that found for Oosterhoff type II clusters, whereas the ratio between first-overtone (RRc) pulsators and the total number of RR Lyrae stars is quite similar to that found in Oosterhoff type I clusters. Based on observations collected at the European Southern Observatory, La Silla, Chile, on Osservatorio Astronomico di Capodimonte guaranteed time.