C# 175 171 167
class P{static void Main(){SendMessage(65535,274,61808,2);}[System.Runtime.InteropServices.DllImport("user32")]static extern int SendMessage(int a,int b,int c,int d);}
A lot of the answers here don't actually make the screen black: on an LCD screen, the backlight remains on and bleeds through, leaving you with a darkish grey.
This little snippet actually tells Windows to turn off the screen, the same as what the inactivity timer does (Note: this doesn't violate the "no power off" rule because it really just causes the monitor to go into standby. Most monitors will turn back on when input is resumed. Also, that rule's intention seems to be to make sure the program can turn it back on - see below.)
Move the mouse or press a key to turn the screen back on.
Monitor power off adapted from http://stackoverflow.com/a/713519/1030702https://stackoverflow.com/a/713519/1030702