Let's say Al Qaeda never tries this audacious attack and instead sticks to pinpricks like the USS Cole.

There is a serious academic work using counter-factuals around what would have happened with Iraq with Gore as President. In it, there is some analysis that says 9-11 changed the American tolerance for bellicose rhetoric about WMDs, something Hussein was apparently bluffing on for domestic and regional political reasons. So if you remove 9-11 you can make a good case for a more limited move on Iraq.

Source: http://www.cambridge.org/ca/academic/subjects/politics-international-relations/international-relations-and-international-organisations/explaining-iraq-war-counterfactual-theory-logic-and-evidence

Without the boost in popularity from 9-11, and then the second boost from the Iraq invasion, and then the third boost from capturing Hussein, it becomes more difficult to see Bush winning in 2004. His margin was razor thin anyway, just 100,000 votes in Ohio. Its reasonable to think Bush would have been defeated.

http://www.hist.umn.edu/~ruggles/Approval.htm

Its also reasonable to argue that John Kerry would not have been the nominee for the Democrats. He was chosen as a war hero and foreign policy stalwart in an election where the Democrats would need those bona fides. Takes away 9-11 and they don't.

On US policy, this all adds up to avoiding military quagmires in Afghanistan and Iraq, higher domestic spending and a stronger economy as a result, and potentially investment in infrastructure and climate change by the 2004-2008 Democrat president. But the 2008 era recession likely proceeds apace, given the bipartisan consensus around liberalization of regulation on Wall Street.

In Britain, Tony Blair would not have risked his career on Iraq, and thus would potentially have had the upper hand against Gordon Brown longer. But the policy implications there are modest.

http://en.wikipedia.org/wiki/Labour_Party_(UK)_leadership_election,_2007

The Middle East is a serious hypothetical impact. Obviously, avoiding the US invasion in Iraq and Afghanistan are huge changes, leaving a Taliban regime in Kabul and a counter-balance to Iran in Baghdad. Syria would have more stability verses the present, given fewer global jihadists using it as a transit point to Iraq.