Depends on what their ultimate goal is.
Is it about spreading fear?
-If so, then yes. They have successfully put the American public in a state of perpetual unease. Americans have put up with increasingly intrusive security measures to ward off a perceived terror threat, regardless of whether it's real or not. The knee jerk invasion of Iraq was also largely based on this fear.
Is it about strengthening Islam in the west
-This is where it gets a bit more debatable. Arguably there is a fear of this religion and this greatly benefits the Jihadists. They have realized through fear they can virtually eliminate any criticism of their culture by simply threatening violence. The Danish cartoon controversy is a good example. That artist has a huge price on his head simply because he dared to mock the prophet. Some folks believe we should censor this type of expression to protect ourselves from harm. So in that case, the terrorists have won. Their belief is the superior one because the west gives it unprecedented special treatment.
On the other hand, it has lead to increased mistrust and harassment of Muslims living in the west.
Is it about spreading Islam?
If so, then they have failed. At least in the broader sense of getting folks to convert to the religion. 9/11 created hoards more atheists than it did Muslims. However, if it's about spreading radical Islam, then it succeeded. The Jihadist movement attracts a lot of disenfranchised young Muslim men. Much in the same way gangs attract young men in America. It gives them a sense of power and belonging. Jihadists prey on their frustrations and turn them into guerrilla warriors.