It's difficult to generalize about this question, but if we select several key events from the past forty years, we can extrapolate patterns that have recurred as a response to terrorist acts.
In 1979, the takeover of the US Embassy in Tehran by radical Islamic students was widely regarded as a terrorist action intended to intimidate the US into extraditing Shah Reza Pahlavi to his home country. This was the beginning of a new polarization, eventually supplanting that of the old Cold War, in which the West (chiefly the US) now took an antagonistic stance toward not only Iran but the Muslim countries overall. But the response by the US primarily took the form of economic sanctions and the freezing of Iranian assets. The military response was weak and ineffective and was aimed only at freeing the hostages rather than attacking and punishing the Iranian state.
In 1983, the terrorist attack on the US Marine Base in Beirut, Lebanon, similarly did not provoke a military response but had the opposite effect of persuading the Reagan administration to withdraw its troops from Lebanon. This was especially ironic given the generally hawkish stance of that administration with regard to the Soviet Union in the last years of the Cold War. Yet the ideological split between West and East was worsened by this event. More and more the US began to view Islamic fundamentalism as a danger to the stability of the "world order." In the war occurring at that time between Iran and Iraq, which lasted from 1980 to 1988, the US implicitly supported Iraq because it was seen as less of a danger than Iran. Despite the 1991 Gulf War and the 1998 bombings in Kenya and Tanzania, terrorism did not cause any further major shakeup of world politics until the 9/11 attacks of 2001, which propelled the US into a series of wars in the Middle East, first in Afghanistan, then Iraq, and eventually Syria. Those wars have both weakened terrorism and, on the other hand, possibly caused more recruits to join the cause of jihad against the West.
More important, perhaps, was the fact that the aggressiveness of the US, especially in Iraq (which had had no involvement in the 9/11 attacks), the bogus claims about "weapons of mass destruction," and the incompetent manner in which the Iraq war was carried out, alienated the other Western countries and weakened the NATO alliance. In each of these situations, the effects of terrorism—whether or not leading to open warfare—were to create or to worsen an antagonistic stance between the US and the new "enemy" supplanting communism. But at the same time, the effects of that new orientation have been inconclusive. No one can say if the US, the Middle East, and the world as a whole are in a worse state now than before these actions occurred. In Iraq, Saddam Hussein was expelled from power and executed, but the Middle East overall may be in worse shape now than before. And the status of the US as the dominant power of the world is ambiguous. Like anything else in history, one must wait decades or even centuries before one can evaluate the success or failure of individual actions, the responses to them, and the wars and treaties that were triggered by them.