I stumbled upon this and have to admit I did not know there is the equivalent of the Windows RUN dialog on Windows Mobile 5 & 6. The RUN box is handy for running applications without going through the menu system and it turns out it works on most devices running those versions of Windows Mobile. To invoke the Windows Mobile RUN box just hold down the ACTION key (usually the center button on the d-pad) and tap and hold the clock icon in the upper right corner of the screen. When you do that you get this box:
This works on Professional (WM6) or Pocket PC (WM5) devices.