The equation of state for asymmetric nuclear matter, the symmetry energy and proton fraction are calculated utilizing the microscopic many-body Brueckner-Hartree-Fock approach using the CD-Bonn and Argonne V18 nucleon-nucleon potentials enhanced with various types of three-body forces. These models are constructed to reproduce the experimental value of binding energy of symmetric nuclear matter. In addition, three-body forces are likely crucial in the case of dense nuclear matter to obtain a stiff equation of state to reproduce the maximum mass of the neutron stars compatible with the measured experimental values.