  Context. Classical Be stars are hot non-supergiant stars surrounded by a
gaseous circumstellar disk that is responsible for the observed infrared-excess
and emission lines. The phenomena involved in the disk formation still remain
highly debated. Aims. To progress in the understanding of the physical process
or processes responsible for the mass ejections and test the hypothesis that
they depend on the stellar parameters, we initiated a survey on the
circumstellar environment of the brightest Be stars. Methods. To achieve this
goal, we used spectro-interferometry, the only technique that combines high
spectral (R=12000) and high spatial ($\theta_{\rm min}$=4\,mas) resolutions.
Observations were carried out at the Paranal observatory with the VLTI/AMBER
instrument. We concentrated our observations on the Br$\gamma$ emission line to
be able to study the kinematics within the circumstellar disk. Our sample is
composed of eight bright classical Be stars : $\alpha$ Col, $\kappa$ CMa,
$\omega$ Car, p Car, $\delta$ Cen, $\mu$ Cen, $\alpha$ Ara, and \textit{o} Aqr.
Results. We managed to determine the disk extension in the line and the nearby
continuum for most targets. We also constrained the disk kinematics, showing
that it is dominated by rotation with a rotation law close to the Keplerian
one. Our survey also suggests that these stars are rotating at a mean velocity
of V/V$_{\rm c}$\,=\,0.82\,$\pm$\,0.08. This corresponds to a rotational rate
of $\Omega/\Omega_{\rm c}$\,=\,0.95\,$\pm$\,0.02 Conclusions. We did not detect
any correlation between the stellar parameters and the structure of the
circumstellar environment. Moreover, it seems that a simple model of a
geometrically thin Keplerian disk can explain most of our spectrally resolved
K-band data. Nevertheless, some small departures from this model have been
detected for at least two objects (i.e, $\kappa$ CMa and $\alpha$ Col).
Finally, our Be stars sample suggests that rotation is the main physical
process driving the mass-ejection. Nevertheless, smaller effects from other
mechanisms have to be taken into account to fully explain how the residual
gravity is compensated.
