How Actively Involved Is God in Our Lives?

I was asked once if I believed in a God who is intimately involved in all aspects of our lives or a God who creates and steps back to let things happen. 

I have experienced directly a few cases of truly miraculous healing. I also have experienced instances of piercing insight regarding things of which I literally was not and could not have been aware. I also have experienced a couple of things that were truly miraculous about which I almost never talk.

Having said that, I have no idea how much God works actively in our lives, but I do believe we can connect to the divine in us much more than most of us do. I see GOD as a big "G" god - and I see us as little "g" gods. I think we fail to understand gods every bit as much as we fail to understand God.