By using a key combination, you can actually make the Run dialog which we are all accustomed to, to show up on Windows Mobile too.
It is really like the one on Windows, and you can add command-line parameters too. (like the one in the picture; you can open IE with a predefined address)
Hold the Action hardware button and then tap and hold the time display at the top right of the screen. When you release the stylus, a menu will popup. Select the Run option and there it is! Enter the full path of any executable on the device with any parameters you may like to give.