We study systematically transport, susceptibility and heat capacity for BaFe$_{2-x}$Co$_x$As$_2$ single crystals. In the underdoped region, spin density wave (SDW) transition is observed in both resistivity and susceptibility. The magnetic susceptibility shows unusual T-linear dependence above SDW transition up to 700 K. With Co doping, SDW ordering is gradually suppressed and superconductivity emerges with a dome-like shape. Electrical transport, specific heat and magnetic susceptibility indicate that SDW and superconductivity coexist in the sample BaFe$_{2-x}$Co$_x$As$_2$ around x = 0.17, being similar with (Ba,K)Fe$_2$As$_2$. When x$>$0.34, the superconductivity completely disappears. A crossover from non-Fermi-liquid state to Fermi-liquid state is observed with increasing Co doping. A detailed electronic phase diagram about evolution from SDW to superconducting state is given.
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