(Click here for Arguments for Fred #3)
The most perfect being imaginable is an all-powerful, all-good, all-knowing, all-present super-being who for the sake of argument we shall call God. Obviously (the argument goes) such a being who actually existed would be more perfect than one we simply imagine, but if he doesn't exist, then in fact we can imagine a being more perfect than the one we previously imagined. That is, if we can imagine a god that exists, it must be more perfect than the "most perfect" one we imagined at the outset, which is a contradiction. So therefore God exists (in order not to have this contradiction). Unfortunately for this argument, it fails to recognise that each of the gods, of varying degrees of perfection, are all being imagined, so even if we imagine a god that exists in reality, it is still only existing in our minds.
See Skeptico's recent blog post and the subsequent comments for further discussion of this aspect of the ontological argument. It pretty much comes down to semantic logic-chopping. James Tracy also has a good summary at AnAtheist.Net. For a more formal description of the ontological argument, try Wikipedia.
Personally I've always found the ontological argument for the existence of God to be the least convincing. I thought the reason for this might be that I didn't understand it, but I've come to the conclusion that it doesn't make sense anyway. Try this variation (thanks to Dan Barker): the most perfect void imaginable is one where nothing, absolutely nothing at all, exists. Obviously, if the existence of the perfect void were actually true, and nothing at all existed, then the actual perfect void would be more perfect than the one that is simply imagined. But this is a contradiction, only resolvable by the actual existence of the perfect void, where nothing at all exists. (Where did everybody go? Why can't I see anything?)
UPDATE 2009-08-31: Click here for AfF #5
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