Many theists in the tradition of Anselm and Aquinas define God as a necessary being. But if God is a necessary being, then he cannot not exist: he exists in all broadly-logically possible worlds. The actual world is of course one of these worlds. So it would seem to follow from the very definition of God favored by Anselmians that God exists. But surely the existence of God cannot be fallout from a mere definition!
I have hammered the Objectivists (Randians) for their terminological mischief as when they rig up 'existence' in such a way that the nonexistence of the supernatural is achieved by terminological fiat. So doesn't fairness demand that I hammer the Anselmians equally? (This is one way of attaching sense to Nietzsche's notion of philosophizing with a hammer, although it is not what he had in mind.)
The trouble with defining God as a necessary being is that 'necessary being' conflates modal status and existence. For any item we ought to distinguish its modal status (whether necessary, impossible, or contingent) from its existence or nonexistence.
The concept of God as "that than which no greater can be conceived" is the concept of a being that exists in every possible world if it exists in any world. But from this one cannot validly infer that God exists. For it might be (it is epistemically possible that) God exists in no world, in which case he would be impossible. God is either necessary or impossible: that was Anselm's great insight. He cannot be a contingent being.
If we want one word to express this disjunctive property of being either necessary or impossible, that word is 'noncontingent.' So we should not say that God is a necessary being. We should say that he is a noncontingent being.
Companion post: Necessary, Contingent, Impossible: A Note on Nicolai Hartmann