In the original X-Com you could basically point your weapon any direction and fire it. You could shoot buildings, vegetation, and even your own men. If you had a strong enough weapon you could shoot through a wall and create an entry into a structure where there wasn't one before. You could also fire in the direction of enemies that you couldn't necessarily see, but which other squad members could see.
The only weapon I've had so far that is free target is the rocket launcher. I'm sorely missing the ability to fire at will. I notice that plasma and laser weapons will destroy walls and cover, but I don't can't seem to be able to fire at anything I want.
For information purposes I'm playing NORMAL: Tutorial mode.
Best Answer
No, unfortunately. The devs said it wasn't possible with the engine back before the game was released.