The long-range correction scheme for the density functional theory, combined with a van der Waals functional, is examined for its applicability to a wide variety of weakly bonded complexes including dispersion, dipole-induced dipole, dipole-dipole, and hydrogen-bonded complexes. The present method is able to describe geometries and binding energies of all these complexes accurately. Explicit inclusion of the long-range exchange and dispersion interactions is found to be important for the balanced description of various kinds of weak interactions. The present method is a promising alternative for high-level ab initio methods in calculations of large and complex systems, because it gives equally correct descriptions for various types of molecular interactions with much less computational cost.