Aims. We investigate the spectral and temporal behavior of the high mass X-ray binary Vela X-1 during a phase of high activity, with special focus on the observed giant flares and off states. Methods. INTEGRAL observed Vela X-1 in a long almost uninterrupted observation for two weeks in 2003 Nov/Dec. The data were analyzed with OSA 7.0 and FTOOLS 6.2. We derive the pulse period, light curves, spectra, hardness ratios, and hardness intensity diagrams, and study the eclipse. Results. In addition to an already high activity level, Vela X-1 exhibited several intense flares, the brightest ones reaching a maximum intensity of more than 5 Crab in the 20-40 keV band and several off states where the source was no longer detected by INTEGRAL. We determine the pulse period to be 283.5320 ± 0.0002 s, which is stable throughout the entire observation. Analyzing the eclipses provided an improvement in the ephemeris. Spectral analysis of the flares indicates that there appear to be two types of flares: relatively brief flares, which can be extremely intense and show spectral softening, in contrast to high intensity states, which are longer and show no softening. Conclusions. Both flares and off states are interpreted as being due to a strongly structured wind of the optical companion. When Vela X-1 encounters a cavity with strongly reduced density, the flux will drop triggering the onset of the propeller effect, which inhibits further accretion, giving rise to off states. The sudden decrease in the density of the material required to trigger the propeller effect in Vela X-1 is of the same order as predicted by theoretical papers about the densities in OB star winds. A similarly structured wind can produce giant flares when Vela X-1 encounters a dense blob in the wind.