Compressible, magnetohydrodynamic (MHD) turbulence in two dimension is studied through high-resolution, numerical simulations with the isothermal equation of state. First, hydrodynamic turbulence with Mach number (M)rms ~ 1 is generated by enforcing a random force. Next, initial, uniform magnetic field of various strengths with Alfvenic Mach number Ma ≫ 1 is added. Then, the simulations are followed until MHD turbulence is fully developed. Such turbulence is expected to exist in a variety of astrophysical environments including clusters of galaxies. Although no dissipation is included explicitly in our simulations, truncation errors produce dissipation which induces numerical resistivity. It mimics a hyper-resistivity in our second-order accurate code. After saturation, the resulting flows are categorized as SF (strong field), WF (weak field), and VWF (very weak field) classes respectively, depending on the average magnetic field strength described with Alfvenic Mach number, (Ma)rms ~1, (Ma)rms≥1, and (Ma)rms ≫ 1. The characteristics of each class are discussed.