  Cygnus X-1 is the archetypal black hole (BH) 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 or 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 Cygnus X-1 optical position. This episode, occurred during a
hard spectral state of Cygnus 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 Cygnus 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
$F_{\gamma,U.L.} = 3 \times 10^{-8} \rm ph cm^{-2} s^{-1}$ 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.
