Density functional theory (DFT) is one of the most widely used electronic structure calculation methods due to its accuracy and practical computation cost. There remain challenges, however, such as anionic systems and radical systems where DFT suffers from the self-interaction error. For systematic error analysis, we decompose the energy error of any variational density functional calculation into errors contributed from the approximate functional and that from the self-consistent Korn-Sham density. In most DFT calculations, the functional error dominates: however, we have found several abnormal cases where the density-driven error dominates. In particular, any self-interaction error can be decomposed this way and many of them, while rare, turned out to be density-driven. We suggest a simple cure for these abnormal calculations, density corrected density functional theory (DC-DFT). DC-DFT is a non-variational DFT which uses more accurate density than the approximate density. One practical way to implement the method is to use the Hartree-Fock density, which has been already known to give remarkably accurate results in some cases. A small HOMO-LUMO gap in DFT calculations leads to large density-driven errors and, thus, may be used as an indicator of abnormal calculations. We discuss examples including simple two electron atom energies, electron affinities of small molecules, dissociation curves, and preferred geometries of ions and radicals in solution.