There's several layers in a screen, the outer layer being used for protection. If you have an LED TV, and the crack is just on the outer layer, you'll be fine, if somewhat upset with a crack. If the crack goes to inner layers, you start getting bleed as heat from the leds starts affecting other leds. If the TV is LCD, same, but the bleed will be because of the liquid, it'll start turning black. If that is a plasma TV, you are on borrowed time. The buffers used to supply the picture will try to put up 1 color per pixel. With a crack, it'll rainbow/prism at those pixels and eventually the buffer board gets overloaded. Dead TV. It's the biggest drawback to Plasmas, cracks always kill the TV. It's just a matter of time.
So depending on the TV type and depending on the amount of damage/depth to the crack will determine usability and life expectancy.