Dealing with the legacy of the attacks is one of Barack Obama's toughest challenges
By Roger Hardy
BBC Middle East and Islamic affairs analyst
Across the United States, the memory of 9/11 - that fateful Tuesday in 2001 when suicide attacks struck New York and Washington - is still very much alive.
This year the annual commemoration of the attacks in the US has been given a new name - the National Day of Service and Remembrance.
President Barack Obama and his wife Michelle have called on Americans to carry out community service as a way of honouring "the heroes of that dark day".
Down but not out
Dealing with the legacy of 9/11 is one of Mr Obama's toughest challenges.
There has been no repeat of 9/11 on American soil - but around the world al-Qaeda and its extended family are still in business.
Three recent events show that the global threat remains real:
- the hotel bombings in the Indonesian capital Jakarta in July
- the assassination attempt in August against the Saudi prince who is in day-to-day charge of his country's internal security
- and the conviction this week of three British Muslims for their involvement in a plot to bomb seven transatlantic airliners in 2006.
Al-Qaeda leaders could still be winning the global battle for hearts and minds
The consensus among most experts is that al-Qaeda is down but not out.
It has been weakened by constant pressure from the US and its allies. Some of its middle-ranking leaders have been killed in US air strikes by pilotless Predator drones.
In two important countries where it once seemed strong - Iraq and Saudi Arabia - it has been pushed on to the defensive.
But the same experts tend to think that, in the global battle for Muslim hearts and minds, al-Qaeda has outperformed its adversaries.
Its ideology still seems to have a potent appeal to disaffected young Muslims around the world.
On the global jigsaw of extremism, the main front is now the remote and lawless region along the Afghan-Pakistani border.
This is not just where Osama Bin Laden and his number two, Ayman al-Zawahiri, are thought to be.
For the jihadists, Afghanistan, Pakistan - and perhaps India - now look more promising terrain than Iraq.
It is here that al-Qaeda and its Taliban allies are stepping up the pressure.
Elsewhere, al-Qaeda "franchises" operate in North Africa, Yemen and south-east Asia.
And, as the airliner plot showed, al-Qaeda continues to target Europe, using young "home-grown" Muslims, including converts.
The Obama effect
But if the picture is broadly familiar, there is one new element in the equation - Barack Obama.
Obama has made outreach to the Muslim world a high priority
His election prompted a fierce attack from the al-Qaeda information machine.
Ayman al-Zawahiri went so far as to use a racist slur, calling the new president a house slave.
This suggested the jihadists saw Mr Obama as a trickier target than his predecessor, George W Bush.
The new president was quick to make outreach to Muslims a priority.
He dropped the term "war on terror" and other language deemed counter-productive.
And in a much-publicised speech at Cairo University in June, he offered Muslims a "new beginning" in their relations with America.
He pledged to withdraw US troops from Iraq by 2012 - and called the situation of the Palestinians "intolerable".
But, three months on, even Muslims who welcomed the speech are sceptical.
They see Israel building more settlements in the West Bank, they hear US officials threaten Iran with "crippling" sanctions and they watch the build-up of American troops in Afghanistan.
"He speaks like Obama," remarked one American Muslim commentator, "but acts like Bush."
While coping with Muslim suspicion of the West, the president also has to deal with the other side of the coin - Western suspicion of Islam.
Many still believe that what's under way is a clash of civilisations.
"The danger posed by Islamists is the gravest threat to the free world since the fall of communism and the earlier crushing of Nazi Germany," wrote Nile Gardiner in the London-based Daily Telegraph this week.
Mr Gardiner works at the Heritage Foundation, a conservative think-tank in Washington.
Challenging extremism, he went on, "is not a temporary law and order exercise, but a long-term war fought for the defence of Western civilisation".
An anonymous comment posted on the Telegraph website reads: "Militant Islam does the dirty work for Islam."
Such sentiments - in stronger or more muted form - are not uncommon.
Students were recently sent home from their school in Florida for wearing T-shirts - supplied by a local church - proclaiming "Islam is of the Devil".
'Narratives of humiliation'
Healing the rift between Islam and the West is a long-term challenge.
Writing in Newsweek, seasoned American diplomat Ryan Crocker ponders the lessons of 9/11, eight years on.
Mr Crocker recently retired after almost four decades in the State Department, serving as US ambassador in Kabul and most recently in Baghdad.
Americans, he writes, have yet to learn that "imposing ourselves on hostile or chaotic societies is no solution".
"The perceived arrogance and ignorance of overbearing powers can create new narratives of humiliation that will feed calls for vengeance centuries from now."
What's needed, he says, is "strategic patience" - something Americans have traditionally "found hard to muster".