Is Existence Necessary?

A student of mine was discussing a debate he viewed concerning the existence of God and the team arguing in favor of the thesis began with an axiom that existence of the universe is a necessary truth.  Is it?  Is it possible that nothing could exist?  If we think about possibility in terms of possible worlds, is the idea of a possible world in which nothing exists possible?  Would such a world be one among the multiplicity of possibilities or is it a non-world, that is, is it logically inconsistent to have a world in which there is no world?  Does there necessarily have to be something?