I remember using EMP grenades in earlier versions to take down Sectopods, Tanks etc. as an alternative to laser weapons - something you can get quite early in the game if you get your research right. As far as i can tell there is no actual reason to use EMP grenades anymore, as almost all enemies are more or less immune to them. The only ones i could find that were actually susceptible to EMP were alien drones and the cyberweb robots, and they can be taken down with conventional weapons.