Context. Observations of very high-energy γ-rays from blazars provide information about acceleration mechanisms occurring in their innermost regions. Studies of variability in these objects lead to a better understanding of the mechanisms in play. Aims. To investigate the spectral and temporal variability of VHE (>100 GeV) γ-rays of the well-known high-frequency-peaked BL Lac object PKS 2155−304 with the HESS imaging atmospheric Cherenkov telescopes over a wide range of flux states. Methods. Data collected from 2005 to 2007 were analyzed. Spectra were derived on time scales ranging from 3 years to 4 min. Light curve variability was studied through doubling timescales and structure functions and compared with red noise process simulations. Results. The source was found to be in a low state from 2005 to 2007, except for a set of exceptional flares that occurred in July 2006. The quiescent state of the source is characterized by an associated mean flux level of (4.32 ± 0.09 stat ± 0.86 syst ) × 10 −11 cm −2 s −1 above 200 GeV, or approximately 15% of the Crab Nebula, and a power-law photon index of Γ = 3.53 ± 0.06 stat ± 0.10 syst . During the flares of July 2006, doubling timescales of ∼2 min are found. The spectral index variation is examined over two orders of magnitude in flux, yielding different behavior at low and high fluxes, which is a new phenomenon in VHE γ-ray emitting blazars. The variability amplitude characterized by the fractional rms F var is strongly energy-dependent and is ∝E 0.19±0.01 . The light curve rms correlates with the flux. This is the signature of a multiplicative process that can be accounted for as a red noise with a Fourier index of ∼2. Conclusions. This unique data set shows evidence of a low-level γ-ray emission state from PKS 2155−304 that possibly has a different origin than the outbursts. The discovery of the light curve lognormal behavior might be an indicator of the origin of aperiodic variability in blazars.