I recently enjoyed watching V for Vendetta. It does a wonderful job of portraying an anarchist's view of the world. The government is oppressive, the most random of destruction would improve things, and, of course, everything you have ever heard all goes together through a long chain of connections.
The most impressive part of it, though, is how well the feeling comes across. It really shows what it feels like to be in a mass, counter-cultural movement. You feel like millions of people are with you and just waiting to rise up. It feels good.
I would imagine that a Muslim suicide bomber might feel the same way. They are thinking that they are part of a great wave of humanity rising up to rise Allah to his former glory. Likewise, I could see people feeling like that as they blow up a bridge or a water plant. They, like V, might well say "the people need a symbol more than they need a little water."
On the other hand, I would imagine that assassins feel differently. Their work is too surgical. V's movement was about random destruction. He says he does not know what will come next, but that things are so bad that he wants to roll the dice and start over. It is different for those who assissinate precisely those governors of Anbar who speak out against Al Qaeda. Assassins fight for specific powers, not for any great wave of humanity.
So what are they thinking? Is it some sort of financial arrangement? Do such assassins hope for power in the new regime? I do not know. What do you think?
The little bit of investigation I have done on this is inconclusive. What I found when looking in the past is that even the scholars on the subject have many different views. Thus, asking how they feel or where they come from is interesting, but ultimately not clarifying. It seems more helpful, if you are interested in international politics, to think about the leaders of these groups than what goes on in the followers' heads. For the leaders, the search for power explains things pretty well, and also suggests ways to respond.