Contrary to what some Muslim terrorist and real ignorant people of Islam think, the greatest Jihad is not fighting with the infidels, bringing people to Islam, or the complete and utter destruction of the west and the United States in particular.
From the Quran itself, "the greatest Jihad" is overcoming your {believers} base desires and thoughts. Ridding yourself of impure thoughts and actions. Somehow this message of peace has been lost in the "holy war" being perpetrated against the west.
There tells a story of Ali, a cousin of Mohammed the Prophet, being locked in battle with an infidel, as Ali went to strike the killing blow his enemy spat on him, Ali threw down his sword and refused to kill his enemy. Ali refused to kill because it was no longer justice he was fighting for but it became personal and he did not want to stand before Allah as a murderer.
The above message would be a good lesson for the Terrorist to read and remember.
Below are a couple links explaining what the greatest Jihad SHOULD be about, not what it is today.
http://www.alislam.org/books/truth/jehad.html
http://cityofbrass.blogspot.com/2003/11/this-post-is-jihad-ii.html