Aims. In order to gain insights into the variability behaviour of the circumstellar (CS) atomic gas, we have analysed 337 multi-epoch optical spectra of 38 Herbig Ae/Be (HAeBe) stars. Methods. Equivalent widths (EWs) and line fluxes of the Hα, O i6300, He i5876 and Na iD lines were obtained for each spectrum; the Hα line width at 10% of peak intensity (W10) and profile shapes were also measured and classified. The mean line strengths and relative variabilities were quantified for each star. Simultaneous optical photometry was used to estimate the line fluxes. Results. We present a homogeneous spectroscopic database of HAeBe stars. The lines are variable in practically all stars and timescales, although 30% of the objects show a constant EW in O i6300, which is also the only line that shows no variability on timescales of hours. The He i5876 and Na iD EW relative variabilities are typically the largest, followed by those in O i6300 and Hα. The EW changes can be larger than one order of magnitude for the He i5876 line, and up to a factor 4 for Hα. The O i6300 and HαEW relative variabilities are correlated for most stars in the sample. The Hα mean EW and W10 are uncorrelated, as are their relative variabilities. The Hα profile changes in  ~70% of the objects. The massive stars in the sample (M∗ > 3   M⊙) usually show more stable Hα profiles with blueshifted self-absorptions and less variable 10% widths. Conclusions. Our data suggest multiple causes for the different line variations, but the O i6300 and Hα variability must share a similar origin in many objects. The physical mechanism responsible for the Hα line broadening does not depend on the amount of emission; unlike in lower-mass stars, physical properties based on the Hα luminosity and W10 would significantly differ. Our results provide additional support to previous works that reported different physical mechanisms in Herbig Ae and Herbig Be stars. The multi-epoch observations we present are a useful tool for understanding the origin of the CS lines and their variability, and to establish distinctions in the physical processes operating in pre-main sequence stars.