We report the doping, temperature, and spatial evolutions of the electronic structure of NaFe(1-x)Co(x)As studied by scanning tunneling microscopy. In the parent state we directly observe the spin density wave gap, which exhibits unconventional features that are incompatible with simple Fermi surface nesting. The optimally doped sample has a single superconducting gap, but in the overdoped regime a novel pseudogaplike feature emerges. The pseudogaplike phase coexists with superconductivity in the ground state, persists well into the normal state, and shows strong spatial variations. The characteristics of the three distinct electronic states revealed here shed important new lights on the microscopic models for the iron-based superconductors.