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 _ { 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 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 _ { c } = 0.82 \pm 0.08 . This corresponds to a rotational rate of \Omega / \Omega _ { 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 .