How deep should blacks be?

[skatalite]

For instance, take any Panasonic or Samsung plasma. They are typically black. Should the blacks on the screen be just as deep, or are they typically lighter and you can tell a difference between the two shades?

Another way of asking is: Are blacks supposed to be so deep that, if you pause on a black screen in a dark room, should you be able to tell the set is on or not?