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We study the characteristics of molecular gas in the central regions of spiral galaxies on the basis of our CO(J=1-0) imaging survey of 20 nearby spiral galaxies using the NRO and OVRO millimeter arrays. Condensations of molecular gas at galactic centers with sizescales < 1 kpc and CO-derived masses M_gas(R<500pc) = 10^8 - 10^9 M_sun are found to be prevalent in the gas-rich L^* galaxies. Moreover, the degree of gas concentration to the central kpc is found to be higher in barred systems than in unbarred galaxies. This is the first statistical evidence for the higher central concentration of molecular gas in barred galaxies, and it strongly supports the theory of bar-driven gas transport. It is most likely that more than half of molecular gas within the central kpc of a barred galaxy was transported there from outside by the bar. The supply of gas has exceeded the consumption of gas by star formation in the central kpc, resulting in the excess gas in the centers of barred systems. The mean rate of gas inflow is statistically estimated to be larger than 0.1 - 1 M_sun/yr. The correlation between gas properties in the central kpc and the type of nuclear spectrum (HII, LINER, or Seyfert) is investigated. A correlation is found in which galaxies with larger gas-to-dynamical mass ratios tend to have HII nuclear spectra, while galaxies with smaller ratios show spectra indicating AGN. Also, the theoretical prediction of bar-dissolution by condensation of gas to galactic centers is observationally tested. It is suggested that the timescale for bar dissolution is larger than 10^8 - 10^10 yr, or a bar in a L^* galaxy is not destroyed by a condensation of 10^8 - 10^9 M_sun gas in the central kpc.