  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.
