We present simultaneous Planck, Swift, Fermi, and ground-based data for 105 blazars belonging to three samples with flux limits in the soft X-ray, hard X-ray, and gamma-ray bands, with additional 5 GHz flux-density limits to ensure a good probability of a Planck detection. We compare our results to those of a companion paper presenting simultaneous Planck and multi-frequency observations of 104 radio-loud northern active galactic nuclei selected at radio frequencies. While we confirm several previous results, our unique data set allows us to demonstrate that the selection method strongly influences the results, producing biases that cannot be ignored. Almost all the BL Lac objects have been detected by the Fermi Large Area Telescope (LAT), whereas 30% to 40% of the flat-spectrum radio quasars (FSRQs) in the radio, soft X-ray, and hard X-ray selected samples are still below the gamma-ray detection limit even after integrating 27 months of Fermi-LAT data. The radio to sub-millimetre spectral slope of blazars is quite flat, with (alpha) approx 0 up to about 70GHz, above which it steepens to (alpha) approx -0.65. The BL Lacs have significantly flatter spectra than FSRQs at higher frequencies. The distribution of the rest-frame synchrotron peak frequency (nu(sup s)(sub peak)) in the spectral energy distribution (SED) of FSRQs is the same in all the blazar samples with (nu(sup s)(sub peak)) = 10(exp 13.1 +/- 0.1) Hz, while the mean inverse Compton peak frequency, (nu(sup IC)(sub peak)), ranges from 10(exp 21) to 10(exp 22) Hz. The distributions of nu(sup s)(sub peak) and nu(sup IC)(sub peak) of BL Lacs are much broader and are shifted to higher energies than those of FSRQs; their shapes strongly depend on the selection method. The Compton dominance of blazars. defined as the ratio of the inverse Compton to synchrotron peak luminosities, ranges from less than 0.2 to nearly 100, with only FSRQs reaching values larger than about 3. Its distribution is broad and depends strongly on the selection method, with gamma-ray selected blazars peaking at approx 7 or more, and radio-selected blazars at values close to 1, thus implying that the common assumption that the blazar power budget is largely dominated by high-energy emission is a selection effect. A comparison of our multi-frequency data with theoretical predictions shows that simple homogeneous SSC models cannot explain the simultaneous SEDs of most of the gamma-ray detected blazars in all samples. The SED of the blazars that were not detected by Fermi~LAT may instead be consistent with SSC emission. Our data challenge the correlation between bolometric luminosity and nu(sup s)(sub peak) predicted by the blazar sequence.