A lot of people think terrorism is a new phenomenon since the term terrorism was only recently used a lot in the media. But actually it's much older than that. The term was first used in 1795 during the French Revolution, but that's not a good way to figure out how old the phenomenon is. I mean, just because a word is 200 years old doesn't mean that the idea the word refers to is 200 years old.
Terrorism is the systematic use of violence from one population to another, in order to instill fear, as a means of bringing about political change. I expect that this sort of thing is as old as civilization.
In history, one case that comes to mind is Islam during it's founder's life, 1,400 years ago. Most Muslims don't know the history and assume that Islam spread by voluntary conversion, since that seems the most logical to people in today's open societies. They are descent people who understand the importance of peace, and so they assume that Islam was peaceful too. But actually it spread by the sword. Kingdoms were given a choice, convert to Islam and come under the rule of Mohamed, or die by the swords of Muslims. And for the kings that did not capitulate to Mohamed's demands, what resulted was Islamic invasions of those kingdoms. So Mohamed instituted a systematic approach of using violence in order to make these kingdoms into provinces of his own nation, which constitutes political change. He justified murder, rape, and theft during his military campaigns -- he said it was for the sake of spreading Islam, a command from Allah. The prophet of Islam boasted, “I have been made victorious with terror".
During this period of military expansion, there were tribes in Arabia who were rejecting Islam, and a law was instituted where apostates were to be given a chance to reaffirm their submission to Allah or be killed -- again a command from Allah. That decree is still being enforced today in some countries. This is a means of instilling fear in the population so that they don't reject Islam -- fear of murder is a strong motivator.
So Mohamed was a terrorist. Not the first terrorist, but definitely one of the worst in history -- if we're counting most deaths as the worst.
To be clear, had those kingdoms initiated violence on the Islamic nation, then Mohamed would have been retaliating in self-defense, which would be good. It would be good because it's a means to restore peace, after the aggressor had already forcefully/involuntarily dragged the victim into war against his will. But that's not what happened. Mohamed sent envoys with his letters to these kingdoms unprovoked,  which is evil.
So terrorism is at least 1,400 years old, but really the fundamental feature underlying terrorism is much much older than that, and it pervades our societies a lot more than most people realize. The most important feature of terrorism is related to the fact that it is involuntary. This can be explained by pointing out how it contrasts with liberalism.
Liberalism says that individuals should be treated equally under the law. One key issue in liberalism is tolerance -- which is about agreeing to disagree without initiating violence. So, under liberalism, things like murder and rape are considered wrong.
Terrorism says that it's ok to initiate violence, as a means of causing political change. So terrorism is intolerance. It contradicts liberalism.
The fundamental feature of terrorism is that it is involuntary, against an innocent person, with the goal of involuntarily causing the victim to submit to the aggressor's will. To help clarify this issue, let's consider the alternative way, which is to help someone to change his mind voluntarily, by rational discussion.
In any given disagreement between two or more people, in order for agreement to be reached, they must find an idea that everybody involved agrees with. Otherwise, they are still in disagreement. And when agreement is reached, it means that one or more of the people involved have changed their minds, which implies that it was voluntary. Now this doesn't require that the people agree on everything. But at the minimum, what is required is that they agree to disagree, in the sense that they don't resort to violence. So rational discussion requires that people willingly change their minds, and it requires that they refuse to initiate violence as a means to end the discussion. So rationality -- the willingness to change one's mind, and the refusal to use involuntary means, is a requirement of each person involved. If just one person involved in the disagreement is being irrational, then agreement cannot be reached.
Dissent is ok
Consider a society where dissent is ok. If a disagreement does not end with agreement, then nobody involved retaliates against another with violence. This is what is known as tolerance. So they "agree to disagree." This means that they still disagree about the issue they were discussing, but they agree on the narrow matter of leaving that disagreement alone without resorting to violence. But, in a society where dissent is not ok, where there is no tradition of tolerance, if a disagreement does not end with agreement, then one or more of the individuals involved may initiate violence in order to force the dissenters to "change" their minds, to force them to obey. Note that I put "change" in quotes because they don't actually change their minds, and instead what they do is change their behavior in an effort to avoid violent retaliation from the aggressor.
Now that we've established the fundamental difference between terrorism and non-terrorism, let's consider how pervasive this idea is in our societies. Who do you know that tries to "change" other people's minds involuntarily? Parents. Many parents will punish their kids for disagreeing with them, as a means of causing them to "change" their minds. But as I said, they don't actually change their minds, and what actually happens is that they change their behavior in an effort to avoid the pain of punishment. Parents will also raise their voices and give ugly facial expressions, as a means of threatening punishment on the child if he doesn't "change" his mind.
I suspect that the tradition of coercing people, with violence and threats of violence, as a means of causing obedience, is older than human civilization. And this tradition still pervades our societies today, even in our most open societies -- even in the USA where the tradition of tolerance is engrained as fundamental principles in our constitution.
Tradition of criticism
Now the tradition of criticism is not a knew thing. The ancient greeks had it, though they lost it later. The tradition of criticism sprang up again in the 1500's or so, resulting in what we now call The Enlightenment. The Enlightenment was many things, and science was one of them -- science has a strong tradition of criticism. Scientists expect to have their ideas criticized by other scientists, and they try their best to make their theories more criticizable, so that flaws can be more easily found.
The Enlightenment resulted in a boom of knowledge growth, one that we are still experiencing today. It started in Italy, but many other cultures have adopted this tradition of criticism since then, and so they too have joined The Enlightenment era.
For people to stop resorting to terrorism, they must adopt the tradition of criticism -- to hash out their differences with discussion instead of violence, criticism instead of intolerance, rationality instead of irrationality, peace instead of war.
Ayaan Hirsi Ali on Terrorism
"Many people in Europe and the US dispute the thesis that we are living through a clash of civilisations between Islam and the west. But a radical minority of Muslims firmly believes that Islam is under siege, and is committed to winning the holy war it has declared against the west. A larger group of Muslims, most of them in Europe and America, believes that acts of terror committed by fellow Muslims will unleash a western backlash against all Muslims indiscriminately. With this collective feeling of being persecuted, many Muslim families living in the west insulate themselves in ghettoes. Within those ghettoes, the agents of radical Islam cultivate their message of hatred and seek foot soldiers to fight as martyrs. Unhappy, disoriented youths in dysfunctional immigrant families make perfect recruits to such a cause. With continuing immigration from the Muslim world and a significantly higher birthrate in Muslim families, this is a phenomenon we ignore at our peril." 
Join me to help finish my Islam book — give honest feedback, get your questions answered, and contribute your own ideas.
[1, 3] _Embrace Islam or Else: Prophet Mohammad's Ultimatums to Foreign Kings_, M. A. Khan. [link: http://mostintolerantreligion.com/2012/06/07/embrace-islam-or-else-prophet-muhammads-ultimatums-to-foreign-kings/]
 Hadith, Bukhari: 4.52. 220
 These wars are called the Wars of Apostasy, or Ridda Wars [link http://en.wikipedia.org/wiki/Ridda_wars]
 Now, whether or not the parent intends to raise his voice as a means of instilling fear doesn't matter. The act of raising one's voice when somebody disagrees with you was designed to cause someone to involuntarily "change" their mind. So just because the parent doesn't see it that way, doesn't mean that the child is not fearful of his parent. My point is that what matters is whether or not the child is scared from the parent's voice being raised, rather than whether or not the parent intends to instill fear.
 _The Beginning of Infinity_, by David Deustch. [link: http://beginningofinfinity.com]
 _Parenting and Reason_, by Elliot Temple. [link: http://fallibleideas.com/parenting-and-reason]
 _Nomad_, by Ayaan Hirsi Ali