One of the classical arguments for the existence of God is called the Cosmological argument. The name refers to the fact that the argument is based on the existence and/or nature of the cosmos (it was first called the Cosmological argument by Immanuel Kant in the 18th century in his Critique of Pure Reason).
There are many variations of the argument. Here's one that's been championed in recent years by philosopher William Lane Craig. It's simple, easy to understand, and enjoying renewed popularity:
UPDATE: Several days ago I cited a column by Eric Metaxas in the Wall Street Journal in which Metaxas expressed his amazement at the examples of fine-tuning scientists have discovered to pervade the universe and which he attributed to a Cosmic Designer. Since then, atheistic cosmologist Lawrence Krauss has responded in a letter to the editor criticizing Metaxas' column.
Another cosmologist, the Australian Luke Barnes, has weighed in on his blog Letters from Nature. He faults Metaxas for sloppiness (though I don't think Barnes' criticisms affect Metaxas' overall argument) and faults Krauss for just being wrong. Readers interested in the exchange are invited to follow the links Barnes provides.