Pretty much anything. The most common application for DGD is still running muds, but there is no reason why it couldn't be used (with appropriate LPC objects) as a httpd for example. DGD itself contains nothing specific to any application, only certain kernel functions (kfuns) which Dworkin felt necessary to LPC object coding, compiling and management, and multiple connections.
This minimalistic philosophy and lack of application specific code allow you to create any look and feel you choose through building around basics written into the auto and driver objects. A classic example of making DGD appear to be something other than an LPMud using this methodology is the LPMOO simulation by Robert Leslie.