The main output file of VASP is the OUTCAR. The vasprun.xml contains similar information but in an xml format. The OSZICAR file contains the total energies of the electronic and ionic SCF steps, and it is useful for the monitoring of the calculation.
Here is a comprehensive list of all important output files:
BSEFATBAND BSE eigenvalues used for "fatband" plots. CHG Contains charge density, lattice vectors and atomic coordinates. Should be used for visualization. CHGCAR Same as CHG but it contains also one-center occupancies. Should be used to restart VASP from existing charge density. CONTCAR Is the updated POSCAR file after each calculation, whether ionic movement was performed or not. DOSCAR Contains DOS and integrated DOS. EIGENVAL Contains Kohn-Sham eigenvalues for each k point after the end of the calculation. ELFCAR Contains electron localization function. IBZKPT Contains k-point coordinates and weights. LOCPOT Contains total local potential in eV. OSZICAR Information on each electronic and ionic SCF step. OUTCAR Main output file. PARCHG Contains partial charge densities. PCDAT Contains the pair correlation function. PROCAR Contains spd and site-projected wave function character. PROOUT Contains projection of wavefunction onto spherical harmonics. REPORT Contains output of various molecular dynamics caculations (umbrella integration, etc.). TMPCAR Contains wavefunction and ionic positions of previous ionic step. vasprun.xml Main output file in xml format. vaspout.h5 Main output file in hdf5 format. Required for the postprocessing with py4vasp. vaspwave.h5 Contains charge density and wave functions when output is directed to hdf5. Wxxxx.tmp Contains diagonal elements of screened exchange in BSE calculations. WAVECAR Binary file containing information such as wave function coefficients, eigenvalues, Fermi weights, etc. WAVEDER Contains derivative of wave functions with respect to k point. WFULLxxxx.tmp Store full screened exchange in BSE calculations. XDATCAR Contains ionic configuration for each output step of molecular dynamics simulations.