The download version of DD supports any resolution your monitor can display, and includes widescreen support.
The disk version of DD has an official maximum resolution of 1024x768; the game itself can be played at higher resolutions, but opening the automap may cause the game to crash (the frequency of which is system dependent). I could play at 1152x864 (text was a little small on my monitor at 1280x960), with an odd crash (rare enough I never remembered to save first, so I ended up reverting to 1024x768); others were fine at 1280x960, etc.
