What is the basis for the idea that God is highly involved in human lives?

A few days ago a family member who is religious told me about an event in her life that she thinks is a miracle. She witnessed a car wreck in front of her, and believes that it is a miracle that it was not them because they had stopped to pray beforehand. The details are not particularly important to this question. I know many people of various religions, but I've only heard similar statements from Christians. I live in the USA so I'm wondering if this is something that is largely cultural (being the most popular religion here) or if there is something particular about Christianity that encourages this? Are there any verses in the Bible which support this kind of hyper-involvement in your life by God? And is there a specific movement or denomination that is particularly supportive of this idea?