Suzaku observations of the blazar OJ 287 were performed in 2007 April 10-13 and November 7-9. They correspond to a quiescent and a flaring state, respectively. The X-ray spectra of the source can be well-described with single power-law models in both exposures. The derived X-ray photon index and the flux density at 1 keV were found to be Γ = 1.65±0.02 and S1keV = 215±5 nJy in the quiescent state. In the flaring state, the source exhibited a harder X-ray spectrum (Γ = 1.50±0.01) with a nearly doubled X-ray flux density of S1keV = 404+6-5nJy. Moreover, significant hard X-ray signals were detected up to 27 keV. In cooperation with Suzaku, simultaneous radio, optical, and very-high-energy γ-ray observations of OJ 287 were performed with the Nobeyama Millimeter Array, the KANATA telescope, and the MAGIC telescope, respectively. The radio and optical fluxes in the flaring state (3.04±0.46 Jy and 8.93±0.05 mJy at 86.75 Hz and in the V-band, respectively) were found to be higher by a factor of 2-3 than those in the quiescent state (1.73±0.26 Jy and 3.03±0.01 mJy at 86.75 Hz and in the V-band, respectively). No notable γ-ray events were detected in either observation. The spectral energy distribution of OJ 287 indicated that the X-ray spectrum was dominated by inverse Compton radiation in both observations, while synchrotron radiation exhibited a spectral cutoff at around the optical frequency. Furthermore, no significant difference in the synchrotron cutoff frequency was found between the quiescent and flaring states. According to a simple synchrotron self-Compton model, the change of the spectral energy distribution is due to an increase in the energy density of electrons with small changes of both the magnetic field strength and the maximum Lorentz factor of electrons.