Electric vs. Gravitational shielding There are great similarities between electric and gravitational fields and, furthermore, a room can be electrically shielded so that there are no electric fields simply by surrounding it with a conductor. Why can't the room be gravitationally shielded? Does it have anything to do with mass?
 A: Although you say that there are great similarities in gravitational and electric fields, there is one thing that is fundamentally different in the two - that gravitational field produced by a mass is always in the same direction(towards the mass) while in case of electric(electrostatic) fields two different kinds of electric charges produce fields in opposite directions. Also any two gravitating masses always attract each other; whereas in case of electric charges, they may attract if they are of the opposite sign or repel each other otherwise. It is precisely this duality of charges and their relation with each other that makes electric shielding by a conductor possible. 
In case of changing electric field outside a shielded room, charges the positive charges move in the direction of the electric field thereby producing their own field in the opposite direction to and thus cancelling the ambient electric field. A similar but exactly opposite thing happens in case of the negative charges on the conducting surface. This, in simple terms, is how electric shielding works. However if there were an ambient gravitational field, whatever movable masses are there in the region concerned will move in the direction of the field but the gravitational field produced by them will aid the ambient gravitational field rather than oppose the ambient gravitational field. This will change the net field in the conductor thus leaving no possibility of shielding.
A: Charuhas got a nice point that gravity is always attractive because mass is always positive. There is a nice article in Wiki for Gravitational Shielding. It has something clear...

The term gravitational shielding refers to a hypothetical process of shielding an object from the influence of a gravitational field. Such processes, if they existed, would have the effect of reducing the weight of an object.

In case of electrostatic shielding, the charges redistribute themselves in an electric field, producing their own field which opposes the applied field. But in the case of gravity, you can't do that (till now). Whenever you place the massive object in the field, the objects attract towards each other and move towards the source of the field, which is not shielding but instead, attracting. Though gravity is a long-range force, the field is much weaker than electrostatic attraction. I don't want to do much calculations, but a simple plugging shows that roughly, electric field is about $10^{40}$ times stronger than that of gravity. So, you can't achieve this effect in many possible ways. That maybe a reason why it's hypothetical...
