Al Qaeda has tried to carry the war to the West, but more effective police forces and a lack of well trained operatives caused many al Qaeda members to be arrested before they could carry out their attacks. The Western police forces were much less complacent about ignoring "inept Arab terrorists" than they were before September 11, 2001.
The Moslem media also made much of Afghanistan, and now Iraq, creating many more volunteers for al Qaeda. This may be true. But without the training camps in Afghanistan, it's difficult to turn these raw recruits into operatives that can evade detection and capture by more alert Western security forces. Other nations that have allowed al Qaeda training to take place (Syria, Sudan, Iran, Iraq, Indonesia), are less hospitable these days. Moreover, the tactic of suicide attacks insures that your attackers don't gain valuable experience by carrying out one operation after another.
Al Qaeda is still out there, still eager to attack and determined to keep trying until they succeed. The problem is that if they keep trying long enough, eventually they will succeed.
Al Qaeda has not given up making suicide attacks, but they have had problems getting their people into position since the United States and other Western nations cracked down on al Qaeda operations after September 11, 2001. The Arab media proclaimed an al Qaeda resurgence in the wake of the Afghanistan campaign. They were right, sort of. The al Qaeda organization inside Afghanistan was destroyed, and several hundred al Qaeda members fled to Pakistan. Others moved to Iran or back to the Persian Gulf. Pakistan already had dozens of active Islamic radical organizations. These groups were mainly fighting India in neighboring Kashmir, although some spent most of their time fighting each other. Since the Pakistani government openly sided with the U.S. against Taliban controlled Afghanistan, the al Qaeda taking shelter in Pakistan saw nothing wrong with launching terror attacks there. Thus the location of the al Qaeda "counterattack" was in a Moslem country already full of Islamic radicals. In 2002 there nine terrorist attacks in Pakistan, leaving 57 people (many foreigners or local non-Moslems) dead. Another major attack was made in Bali, Indonesia, as well as some smaller attacks in the Philippines. Indonesia already had an active al Qaeda presence that the Indonesian government was reluctant to crack down on, at least until 181 people were killed by the Bali bombing. The Philippines bombings were done with, perhaps, some al Qaeda technical assistance. But the animosity between Moslems and Christians in the Philippines goes back several centuries.