We present U,B,V,I photometry of the Carina dwarf spheroidal galaxy, based on more than 4,000 CCD images. Special attention was given to the photometric calibration, and the precision for the B,V,I bands is better than 0.01 mag. We compared in the V,B-V and V,B-I color-magnitude diagrams (CMDs) Carina with three Globular Clusters (GCs, M53, M55, M79). We find that only the more metal-poor GCs (M55, [Fe/H]=-1.85; M53, [Fe/H]=-2.02 dex) provide a good match with the Carina giant branch. We performed a similar comparison in the V,V-I CMD with three SMC intermediate-age clusters (IACs, Kron3, NGC339, Lindsay38). We find that the color extent of the SGB of the two more metal-rich IACs (Kron3, [Fe/H]=-1.08; NGC339, [Fe/H]=-1.36 dex) is smaller than the range among Carina's intermediate-age stars. However, the ridge line of the more metal-poor IAC (Lindsay38, [Fe/H]=-1.59 dex) agrees quite well with the Carina intermediate-age stars. These findings indicate that Carina's old stellar population is metal-poor and seems to have a limited spread in metallicity (Delta [Fe/H]=0.2--0.3 dex). Carina intermediate-age stars can hardly be more metal-rich than Lindsay38 and its spread in metallicity appears modest. We also find that the synthetic CMD constructed assuming a metallicity spread of 0.5 dex for intermediate-age stars predicts evolutionary features not supported by observations. The above results are at odds with recent spectroscopic investigations suggesting that Carina stars cover a broad range in metallicity (Delta [Fe/H]~1--2 dex). We present a new method to estimate the metallicity of complex stellar systems using the difference in color between the red clump and the middle of the RR Lyrae instability strip. The observed colors of Carina's evolved stars indicate a metallicity of [Fe/H]=-1.70+-0.19 dex, which agrees quite well with spectroscopic measurements. ; Comment: Accepted on PASP, 12 pages, 6 figures