We present maps of atomic carbon [C I](P-3(1) -> P-3(0)) and [C I](P-3(2) -> P-3(1)) emission (hereafter [C I] (1-0) and [C I] (2-1), respectively) at a linear resolution similar to 1 kpc scale for a sample of one H II, six LINER, three Seyfert, and five starburst galaxies observed with the Herschel Space Observatory. We compare spatial distributions of two [C I] lines with that of CO J = 1 -> 0 (hereafter CO (1-0)) emission, and find that both [C I] lines distribute similarly to CO (1-0) emission in most galaxies. We present luminosity ratio maps of L[C I](1-0)'/LCO(1-0)', L[C I](2-1)'/LCO(1-0)', L[C I](2-1)'/L[C I](1-0)' (hereafter R-[C I] and 70-to-160 mu m far-infrared color of f(70)/f(160). L[C I](2-1)'/LCO(1-0)', R-[C I] and f(70)/f(160) are centrally peaked in starbursts; whereas they remain relatively constant in LINERs, indicating that star-forming activity can enhance carbon emission, especially for [C I] (2-1). We explore the correlations between the luminosities of CO (1-0) and [C I] lines, and find that LCO(1-0)' correlates tightly and almost linearly with both L[C I](1-0)' and L[C I](2-1)', suggesting that [C I] lines, similar to CO (1-0), can trace total molecular gas in H II, LINER, Seyfert, and starburst galaxies on kpc scales. We investigate the dependence of L[C I](1-0)'/LCO(1-0)', L[C I](2-1)'/LCO(1-0)' and [C I] excitation temperature, T-ex, on dust temperature, T-dust, and find noncorrelation and a weak and modest correlation, respectively. The ratio of L[C I](1-0)'/LCO(1-0)' stays a smooth distribution in most galaxies, indicating that the conversion factor of [C I] (1-0) luminosity to H-2 mass (X[CI](1-0)) changes with CO (1-0) conversion factor (alpha(CO)) proportionally. Under optically thin and local thermodynamical equilibrium assumptions, we derive a galaxy-wide average carbon excitation temperature of T-ex similar to 19.7 +/- 0.5 K, and an average neutral carbon abundance of X [CI]/X [H-2] similar to 2.5 +/- 1.0 x 10(-5) in our resolved sample, which is comparable to the usually adopted value of 3 x 10(-5), but similar to 3 times lower than the carbon abundance in local (ultra)luminous infrared galaxies. We conclude that the carbon abundance varies in different galaxy types.