  Using a holographic proposal for the entanglement entropy we study its
behavior in various supergravity backgrounds. We are particularly interested in
the possibility of using the entanglement entropy as way to detect transitions
induced by the presence horizons. We consider several geometries with horizons:
the black hole in $AdS_3$, nonextremal Dp-branes, dyonic black holes
asymptotically to $AdS_4$ and also Schwarzschild black holes in global $AdS_p$
coordinates. Generically, we find that the entanglement entropy does not
exhibit a transition, that is, one of the two possible configurations always
dominates.
