If you consider the God of the bible to be real (talking about Christianity), then the existence of God is relevant to you because he can do miracles, change your life for the best, and allow you to experience eternal happiness in heaven. The same thing applies to some or most other similar religions.
However, since there is no real proof of God actually interfering with people’s lives directly and granting certain desires that people might’ve expressed through prayer, and there is no proof to confirm the existence Heaven or Hell, we can safely assume that there are no things such as holy miracles, and there is no eternal life following death.
So if we conclude that God does not perform miracles and does not grant access to eternal life in heaven then what is the point of even considering the existence of God?
If God does not interfere with my life in a way that I can somehow influence, then what is the point of even bothering to think about God? I mean, if he does not influence my life, then he's of no importance to me. And if he does influence my life, but I have no influence over his decisions, then even though he is of some importance to me because he affects my life, is still all random, as I cannot predict or influence how God will act. So why would I bother to consider his existance?
As Jon Ericson pointed out below, the view I am describing is Deism. I basically make two assumptions: 1. I reject all religious ideologies. 2. I give credit for the formation of life and the universe to a higher power (God) that by design allows only natural processes to govern creation. (Deism).
Considering the assumptions right, then how is the existence of such a God relevant to me? How can I improve my life by understanding him? If I can only know God through reason and the observation of nature (as deism claims) why would I bother to teach my children about the existence of a God? Why would I not stop my reasoning at saying that the world works by the rules of nature and that is all there is to it. Why would I need to know God in such a case?