It was criticised initially by some of his contemporaries, but continued to fuel others' thought - later it was taken up by philosophers such as Descartes, Spinoza & Leibniz and criticised again by thinkers such as Hume & Kant. I was particularly struck by Kant's criticism, which is that existence is not a predicate - he was answering in particular the formation of the argument that is saying that if God is the most perfect incarnation of all things (ie is perfectly knowing, is perfectly powerful etc), then he must necessarily also be perfectly existing as that is a quality that such a being must have. Kant was saying that existence isn't a quality like the others - so you can describe an object, perhaps it is tall, blue and hairy. And then you can ask the question "and does it exist?", this is a separate question to idea of what the object or concept is.
I can see the seductiveness of the Ontological Argument - both to bolster one's own faith and to say to others "but you must believe, see I have proven it's true!". But to be honest it felt circular to me - it involved first defining God in such a way that his existence was part of the definition, and then saying "and therefore he exists". I'm sure there are more subtleties to the idea than that, however, otherwise it wouldn't've occupied so many people's thoughts for so long.