Aims: As a new approach to the study of resolved stellar populations in nearby galaxies, our goal is to demonstrate with a pilot study in NGC 300 that integral field spectroscopy with high spatial resolution and excellent seeing conditions reaches an unprecedented depth in severely crowded fields. Methods: Observations by MUSE with seven pointings in NGC 300 have resulted in data cubes that are analyzed in four ways: (1) Point spread function-fitting 3D spectroscopy with PampelMUSE, as already successfully pioneered in globular clusters, yields de-blended spectra of individually distinguishable stars, thus providing a complete inventory of blue and red supergiants, and asymptotic giant branch (AGB) stars of type M and C. The technique is also applicable to emission line point sources and provides samples of planetary nebulae (PNe) that are complete down to m5007 = 28. (2) Pseudo-monochromatic images, created at the wavelengths of the most important emission lines and corrected for continuum light with the P3D visualization tool, provide maps of H II regions, supernova remnants (SNR), and the diffuse interstellar medium (ISM) at a high level of sensitivity, where also faint point sources stand out and allow for the discovery of PNe, Wolf-Rayet (WR) stars, etc. (3) The use of the P3D line-fitting tool yields emission line fluxes, surface brightness, and kinematic information for gaseous objects, corrected for absorption line profiles of the underlying stellar population in the case of Hα. (4) Visual inspection of the data cubes by browsing through the row-stacked spectra image in P3D is demonstrated to be efficient for data mining and the discovery of background galaxies and unusual objects. Results: We present a catalog of luminous stars, rare stars such as WR, and other emission line stars, carbon stars, symbiotic star candidates, PNe, H II regions, SNR, giant shells, peculiar diffuse and filamentary emission line objects, and background galaxies, along with their spectra. Conclusions: The technique of crowded-field 3D spectroscopy, using the PampelMUSE code, is capable of deblending individual bright stars, the unresolved background of faint stars, gaseous nebulae, and the diffuse component of the ISM, resulting in unprecedented legacy value for observations of nearby galaxies with MUSE. Based on observations obtained at the Very Large Telescope (VLT) of the European Southern Observatory, Paranal, Chile (ESO Programme ID 094.D-0116(A), 094.D-0116(B), 095.D-0173(A)).The full version of Tables 6, 9 and the reduced dat-acube (FITS file) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/618/A3