The Landau gauge quark propagator in momentum space is investigated using the O(a)-improved Sheikholeslami-Wohlert quark action with a tree-level mean-field improved coefficient csw . We study the unimproved definition of the quark propagator, as well as two different tree-level O(a)-improved propagators. The ultraviolet behavior of the free lattice propagator is studied for each of these in order to establish which of them provides the most reliable description of the quark propagator up to the medium momentum regime. A general method of tree-level correction is introduced. This exploits asymptotic freedom and removes much of the trivial lattice artifacts at medium to high momenta. We obtain results for the quark propagator which are qualitatively similar to those typically used in quark models. A simple extrapolation of the infrared quark mass M(p250) to the chiral limit gives 29868630 MeV, which is consistent with phenomenological expectations.