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We investigated the multifrequency spectral properties of complete samples of three different kinds of blazars, all observed with the ROSAT PSPC in pointed mode. These include the 1 Jy sample of radio-selected BL Lacs (RBLs), the Einstein Extended Medium Sensitivity Survey sample of X- ray-selected BL Lacs (XBLs), and a small but complete sample of flat spectrum radio quasars (FSRQs) from the S5 radio survey. We compared their spectral energy distributions from the radio through the X-ray bands using the ROSAT data and nonsimultaneous radio, infrared, and optical fluxes from the literature. The individual spectral energy distributions in the rest-frame log HERE(νL<SUB>nu</SUB>_) versus log ν representation were fitted with a parabolic function, in order to estimate the bolometric luminosities and peak emission frequencies of each source. We find that the spectral energy distributions of the three kinds of blazars are different but essentially continuous: XBLs and FSRQs occupy separate regions in broadband color-color diagrams, while RBLs bridge the gap between the two populations. Describing the shape of the optical-to-X-ray continua with the composite spectral index α_OX_ - α_X_, for which positive or negative values indicate concave or convex spectra, respectively, we find that the optical-to-X-ray continua tend to be convex for XBLs and concave for FSRQs, while the RBL sample contains objects with XBL-like and with FSRQ-like spectra. For the three samples combined, the spectral index connecting the radio and optical bands, α_RO_, is strongly correlated with α_OX_ - α_X_ and with the bolometric luminosity or redshift, in the sense that sources with steeper α_RO_ are more luminous (distant) and have concave optical-to-X-ray shapes. This shows that the continuum emission of blazars can be characterized by essentially one parameter and suggests that the spectral shape is fundamentally connected to the bolometric luminosity and/or redshift. We discuss the physical parameters deduced for the different blazar classes assuming relativistically beamed synchrotron and inverse-Compton radiation from a homogeneous emission region and from an inhomogeneous jet. We show that the observed sequence of spectral properties of blazars cannot be easily accounted for in terms of a sole change in viewing angle but requires instead a systematic change of intrinsic physical parameters, such as magnetic field, jet size, and maximum electron energy. The change is in the sense that XBLs have higher magnetic fields/electron energies and smaller sizes than radio-selected blazars.