Cygnus X-1 (Cyg X-1) is the archetypal black hole binary system in our Galaxy. We report the main results of an extensive search for transient gamma-ray emission from Cygnus X-1 carried out in the energy range 100 MeV-3 GeV by the AGILE satellite, during the period 2007 July-2009 October. The total exposure time is about 300 days, during which the source was in the "hard" X-ray spectral state. We divided the observing intervals in 2-4 week periods, and searched for transient and persistent emission. We report an episode of significant transient gamma-ray emission detected on 2009 October 16 in a position compatible with Cyg X-1 optical position. This episode, which occurred during a hard spectral state of Cyg X-1, shows that a 1-2 day time variable emission above 100 MeV can be produced during hard spectral states, having important theoretical implications for current Comptonization models for Cyg X-1 and other microquasars. Except for this one short timescale episode, no significant gamma-ray emission was detected by AGILE. By integrating all available data, we obtain a 2 sigma upper limit for the total integrated flux of F-gamma,F-U.L. = 3 x 10(-8) ph cm(-2) s(-1) in the energy range 100 MeV-3 GeV. We then clearly establish the existence of a spectral cutoff in the energy range 1-100 MeV that applies to the typical hard state outside the flaring period and that confirms the historically known spectral cutoff above 1 MeV.
