Terrorism is generally defined as the use of violence to achieve a political goal. However, there is not a unified consensus on the definition of the term terrorism. The UN, for example, has yet to reach an official consensus.
Here is the NATO definition:
The unlawful use or threatened use of force or violence, instilling fear and terror, against individuals or property in an attempt to coerce or intimidate governments or societies, or to gain control over a population, to achieve political, religious or ideological objectives.
And the United Nations Security Council definition (United Nations Security Council Resolution 1566):
criminal acts, including against civilians, committed with the intent to cause death or serious bodily injury, or taking of hostages, with the purpose to provoke a state of terror in the general public or in a group of persons or particular persons, intimidate a population or compel a government or an international organization to do or to abstain from doing any act, which constitute offences within the scope of and as defined in the international conventions and protocols relating to terrorism, are under no circumstances justifiable by considerations of a political, philosophical, ideological, racial, ethnic, religious or other similar nature.
Generally, definitions of terrorism include political, religious or ideological motives, but not all definitions. Most definitions however will include the use of violence, fear, and coercion against individuals, property, and combatants/non-combatants alike.
In all honesty, terrorism does not have a universally recognised definition, and not everyone would agree that all terrorism by definition has a political objective, however many WOULD consider this to be the case.
The best answer to this would be, generally yes they do have political objectives, but not always.
Some additional links:
European Parliament -
Why it is Not Easy For the United Nations to Define Terrorism
Terrorism Act 2000 - UK Legislation