Using the ARO KP 12 m telescope, we have carried out a CO(1–0) and 13CO(1–0) survey of the central regions of 113 “normal” spiral galaxies (i.e., unperturbed and with little or no nuclear activity). Our sample spans the whole range of morphological types (T = 1–7), with distances up to 75 Mpc. The detection rates for the observed objects are 99.1% for CO(1–0) and 75.2% for 13CO(1–0), respectively. For three of the targets in our sample (i.e., NGC 0891, NGC 2903, and NGC 3521), we also carry out 13CO(1–0) mapping along their major axes, which, combined with data from the literature, reveal differences in their molecular gas properties. Analysis of the beam-matched line intensity ratios of CO(1–0)/13CO(1–0) (hereafter {R}1312) indicates that for “normal” spiral galaxies the scatter in {R}1312 is of ≈x3, and has an average value (including upper limits) of 10.4 ± 0.4 (in contrast with the values of 3–5 in typical giant molecular clouds and 13 ± 6 in Starburst Galaxies). No significant correlations (at the ≥2σ level) are found between {R}1312 and the total far-infrared (FIR) luminosity, the FIR colors, and the fraction of area sampled in the disk of each galaxy. There is a tentative (1.4σ significance) correlation between {R}1312 and morphological type along the Hubble sequence. The observed scatter in {R}1312 can be explained by intrinsic variations among the CO conversion factors. The observations presented in this work, which include the most extensive 13CO(1–0) extragalactic survey published so far on “normal” spiral galaxies are ideally suited for use in recovering the “missing” flux of interferometers with elements of similar dish sizes.