We present experimental investigations on the lasing modes in two-dimensional (2-D) hexagonal cavities defined by photonic crystals on slab waveguide structures. The far-field emission patterns and near-field intensity distributions of the lasing modes are analyzed in polarization-resolved 2-D angular distribution measurements and spectrally resolved near-field scanning optical microscopy. The far- and near-field analyses result in identification of the various lasing modes and their subsequent classification into one- and two-dimensional modes. In the one-dimensional modes oscillating between two parallel boundaries of the cavities, longitudinal and transverse modes are identified and found to have transverse-electric polarization. In the two-dimensional modes oscillating two-dimensionally in the cavities, various modes including whispering-gallery-like modes are observed and found to exhibit various polarization states.