What do the Iraqi insurgents want?

Rather than employing the classic rebel tactic of provoking the foreign
forces to use clumsy and excessive force and kill civilians, [the Iraqi rebels] are
cutting out the middleman and killing civilians indiscriminately
themselves, in addition to more predictable targets like officials of
the new government. Bombings have escalated in the last two weeks, and
on Thursday a bomb went off in heavy traffic in Baghdad, killing 21
people.

More generally, the insurgency does not appear to have put forward any program or unifying vision; read more here

I have no particular expertise on the empirics, but from a game-theoretic point of view I can think of seven possible "strategies" at work:

1. Chaos is seen as a path to a new Sunni dictatorship.

2. The goal is not to impose a particular solution on Iraq, but rather to punish the U.S. for intervening, by making matters look bad. 

3. The attacks are fundraising events, just as one might hold a cocktail party for donors.  They help the rebels attain focality and make the headlines; the attacks are not domestic political tactics per se

4. Deliberate amorphousness is the best strategy against a determined and powerful United States.  U.S. public opinion must not be able to identify a discernible enemy.  Perhaps the U.S. is most likely to quit Iraq if we view the Iraqis as "crazy," or "not deserving of freedom."  We are less likely to stop thinking about a visible opponent, such as bin Laden.

5. Unlike Bob Lucas’s modeled rational expectations agents, Iraqi insurgents do not hold the "true economic model" in their heads.  Young men at war are notoriously overconfident.  Just as some al Qaeda members thought the U.S. was a weaker opponent than the Soviet Union, the Iraqi insurgency has some similarly crazy view of the world.  What we perceive as failure simply does not deter them much.

6. The insurgency is smaller than we think.  The violent actions we observe are the "noise" of a minority within a minority.  There is no rational explanation, but we had underestimated how much havoc a small group can wreak.

7. The insurgents are simply mad (how’s that for high-powered game theory?), read Jane Galt.

Unfortunately, all of these are possible, and in various combinations.  Nor do they point to any common direction in terms of policy recommendations for a response.