1. God is the greatest being that we can imagine.Technically, this only proves that God is the greatest being that we can imagine and that, if we imagined God, we have to imagine that God exists. But imaging God's existence isn't proof that God does, in fact, exist. To address this we'd have to add premises like "to exist in reality is greater than to exist in the mind." Regardless, you get the basic idea.
2. To exist is greater than not to exist.
3. Therefore, God exists.
Few find the ontological arguement persuasive. It seems too cute and quick. Seems a bit fishy. And yet, some find the argument persuasive and the argument has been given a fair amount of logical and philosophical attention, then as now.
Personally, I'm one of those who don't find the ontological argument persuasive. And yet, how I think about God has a family resemblance to the ontological argument.
At its heart the ontological argument has us imagine a horizon of "greatness" and "perfection." The argument then goes on to say that existence must be, necessarily, a part of that vision. Maybe, maybe not. But in one sense it really doesn't matter. Because I think that horizon of "greatness" and "perfection" can do much of the work we want from any conception of God, with or without existence.
For example, when I think of "the Kingdom of God" what I have in mind is an ideal, a biblical ideal, a place where swords are beaten in plowshares and where the lion lays down with the lamb. Once posited, this ideal creates two eschatological functions, one negative and the other positive. Negatively, the Kingdom of God damns and stands in prophetic judgment of the status quo. In relation to the Kingdom of God the world is deemed fallen, sinful, and in need of rehabilitation. The horizon of the Kingdom of God creates the "oracle of the Lord," the "thus saith the Lord" of divine wrath and judgment.
Positively, the Kingdom of God functions as a goal state, a telos, a moral North Pole. A vision so beautiful, captivating, and wonderful that it infuses our dreams, our art and poetry, generation after generation.