  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. Our unique data set has allowed 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
Fermi-LAT, whereas ~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-mm spectral slope of blazars is quite flat up to ~70GHz, above
which it steepens to <\alpha>~-0.65. BL Lacs have significantly flatter spectra
than FSRQs at higher frequencies. The distribution of the rest-frame
synchrotron peak frequency (\nupS) in the SED of FSRQs is the same in all the
blazar samples with <\nupS>=10^13.1 Hz, while the mean inverse-Compton peak
frequency, <\nupIC>, ranges from 10^21 to 10^22 Hz. The distributions of \nupS
and of \nupIC of BL Lacs are much broader and are shifted to higher energies
than those of FSRQs and strongly depend on the selection method. The Compton
dominance of blazars ranges from ~0.2 to ~100, with only FSRQs reaching values
>3. Its distribution is broad and depends strongly on the selection method,
with gamma-ray selected blazars peaking at ~7 or more, and radio-selected
blazars at values ~1, thus implying that the assumption that the blazar power
is dominated by high-energy emission is a selection effect. Simple SSC models
cannot explain the 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 \nupS predicted by the blazar sequence.
