The charge transport of serially coupled quantum dots (SCQD) connected to the metallic electrodes is theoretically investigated in the Coulomb blockade regime. A closed-form expression for the tunneling current of SCQD in the weak interdot hopping limit is obtained by solving an extended two-site Hubbard model via the Green's function method. We use this expression to investigate spin current rectification, negative differential conductance, and coherent tunneling in the nonlinear response regime. The current rectification arising from the space symmetry breaking of SCQD is suppressed by increasing temperature. The calculation of SCQD is extended to the case of multiple parallel SCQDs for studying the charge ratchet effect and SCQD with multiple levels. In the linear response regime, the functionalities of spin filter and low-temperature current filter are demonstrated to coexist in this system. It is further demonstrated that two-electron spin-singlet and -triplet states can be readily resolved from the measurement of the Seebeck coefficient rather than that of electrical conductance.