There are mainly two reasons... i feel 1. They want to show their power to the world and want to be the ruler of the world. 2. They have an eagle eye towards the oil producing countries- Mainly arabian countries. so they want all arabian couuntries to be rules by someone who follows their likes. Remember once America had supported Saddam Hussain. But saddam wanted to be a Ruler of Arabia.So US didnt like that. Result....
But ... let me tell you one thing.. It is not that they love their life or not. It is their experience with terrorist leaders whom they follow. Look .. if anyone practice to do so they also dont hesitate to lose their life. That's all they think about life. I think those who follow holy khuran never follow the path of terrorism.