Non-invasive magnetic field sensing using optically-detected magnetic resonance of nitrogen-vacancy centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, elemental Pb and Nb, and compound LuNi2B2C and unconventional iron-based superconductors Ba1−x KxFe2As2 (x=0.34 optimal hole doping), Ba(Fe1−x Cox)2As2 (x=0.07 optimal electron doping), and stoichiometric CaKFe4As4, using variable-temperature confocal system with diffraction-limited spatial resolution. Magnetic induction profiles across the crystal edges were measured in zero-field-cooled and field-cooled conditions. While all superconductors show nearly perfect screening of magnetic fields applied after cooling to temperatures well below the superconducting transition, Tc, a range of very different behaviors was observed for Meissner expulsion upon cooling in static magnetic field from above Tc. Substantial conventional Meissner expulsion is found in LuNi2B2C, paramagnetic Meissner effect is found in Nb, and virtually no expulsion is observed in iron-based superconductors. In all cases, good correlation with macroscopic measurements of total magnetic moment is found.