Yes it is pretty much possible. The real need is the education. All countries should leave in peace and harmony. One country shouldn't interfere in other country's matter. If every government would provide it's citizens the basic rights of education, health, employment and security then there will be no violence and terrorism.
Yes, terrorism can be stopped, but it will take years if not decades. From what I've read, the chief driver of terrorism is poverty. This could be caused by numerous things, but it revolves around poor governance (including a lack of government accountability in the majority of poor nations), leading to corruption, crime and a belief that life can only get worse. Only with better governance, rising incomes and improving quality of life will people moderate their views and turn their backs on terrorism.
Terrorism can be stopped
You can never win a war when you are dealing with religious beliefs. Some terrorist believe they are part of a religious war "JIHAAD" (sp) if they are killed they are considered martyrs and they go to heaven and are given seven virgins... So no it can never be won. However if the US would stop interfering in other peoples business it would be better...