High-quality, blue-violet spectroscopic data are collected for 24 stars that have been classified as type O3 and that display the hallmark N IV and N V lines. A new member of the class is presented; it is the second known in the Cyg OB2 association, and only the second in the northern hemisphere. New digital data are also presented for several of the other stars. Although the data are inhomogeneous, the uniform plots by subcategory reveal some interesting new relationships. Several issues concerning the classification of the hottest O-type spectra are discussed, and new digital data are presented for the five original O3 dwarfs in the Carina Nebula, in which the N IV, N V features are very weak or absent. New spectral types O2 and O3.5 are introduced here as steps toward resolving these issues. The relationship between the derived absolute visual magnitudes and the spectroscopic luminosity classes of the O2-O3 stars shows more scatter than at later O types, at least partly because some overluminous dwarfs are unresolved multiple systems, and some close binary systems of relatively low luminosity and mass emulate O3 supergiant spectra. However, it also appears that the behavior of He II λ4686, the primary luminosity criterion at later O types, responds to other phenomena in addition to luminosity at spectral types O2-O3. There is evidence that these spectral types may correspond to an immediate pre-WN phase, with a correspondingly large range of luminosities and masses. A complete census of spectra classified into the original O3 subcategories considered here (not including intermediate O3/WN types or O3 dwarfs without N IV, N V features) totals 45 stars; 34 of them belong to the Large Magellanic Cloud and 20 of the latter to 30 Doradus.