The most obvious answer is this: throw it. But those who practice such things and a bit of time to spend on, you can find a different way to take advantage of the hardware remained.
After all, if it is only the screen to be damaged, perhaps for a fall or a blow to the corner, you can still count on the motherboard and on the doors, and with them, the ability to play videos, music and games on a TV outside.
I write inspiration from an article published over the weekend by Nate Hoffelder (which, bad luck. It broke the display of a Hisense Sero 7 Pro, 7 inches-like Nexus 7 with Tegra 3) to ask what to do with a tablet with a damaged panel, even in the case that it is impossible to use with the touch screen. Have your say and suggested examples of use in the comments (they are free, registration is not mandatory). I think we should, first of all, understand if the tablet in question has HDMI output or not.
Tablet with HDMI video output.
In this case, it is easy to imagine it as a media player for the living room, maybe hidden in a drawer or attached to the back of the TV. If it is an Android model, then the system will tune to only output video and show the Android interface on your TV. And then from there, perhaps with the help of a special type controller the new Rii mini i28 (but maybe a mouse) you could manage as a common Mini PC Android. Playing video, audio, gaming, maybe XBMC to make it home media center and web browsing would not be a problem.
Still, it is a model with Intel or with one of the supported ARM SoC, it could have a second life on the desk or on the back of a monitor with mouse, keyboard and a nice Linux distro on it. And once this is done, it could become anything given the flexibility of the operating system.
Tablet with no video output.
Here it becomes all the more difficult. It is mandatory to have a screen visible to the management UI and maybe even the touchscreen panel still working, the interface can be controlled with a controller, but if you cannot see anything, and you do not have a video output becomes a … enterprise. You could use Aircast to have at least video playback on a TV, but the tablet should be recent and support this feature.
More recommended to use as a media server or audio player. If the tablet has a microSD reader or microUSB OTG port, you could connect an external drive or a card with inside files and music, install a DLNA server and then take advantage of its wireless connectivity to access the content. A sort of small NAS, absolutely at low power, you can better in many ways with a little of study and research.
Or, using the headphone output, you could connect to the speakers and matched to type Spotify app or web radio to make a HiFi Android. With a DLNA client could read music from a NAS or a network share, and act as a dedicated amplifier for the speakers. Again, with practice and creativity, you could place within a particular frame.
Other ideas and suggestions.
If the tablet has a quality camera still functions could become a video surveillance system based on Android. The app to make it out there, and have all functions of motion detection, sending notifications via the Internet, maybe an audible alarm, and more. There really are a lot of possibilities and, even here, there is nothing to reassemble them into a more suitable frame (perhaps inside a vintage camera not working bought two to money markets).
Finally, we are talking about a mobile device, why not take advantage of its battery to make it portable to take with a file server in during a video conference? If configured properly, it could be some sort of NAS Wireless Travel, autonomous and probably with a few hours of charging, suitable for the small share documents, presentations, images or audio tracks.