The first (western) ontological argument was created by St Anselm (although he is not the only philosopher to have offered such a argument, and some earlier Muslim philosophers formulated similar arguments), who is also considered the father of the Scholastic tradition. Anselm's argument is the most famous of the ontological arguments (although it has its problems). Kurt G?del offered something like Anselm's argument, and his version is very interesting. His version is created on the firm ground of modal-logic. But in order to avoid confusion, I will deal only with Anselm's argument (which was the first western presentation of the argument, and is the argument mostly in mind when the ontological argument is made reference to). First let me state a basic family resemblance (to use Wittgenstein's words) between all ontological arguments. These arguments try to prove God's existence by purely a priori means. In other words, these arguments utilize only reason. In explaining Anselm's argument I will ignore the debate surrounding what the argument was really meant to do. Many think that the account givin of Anselm's argument in traditional books on the history of philosophy are wrong. I will not discuss these unconventional views of what Anselm meant (again) to avoid confusion, not because the traditional account of what Anselm meant is right. Now to the ontological argument. Here is the argument of Anselm.
"Thus even the fool is convinced that something than which nothing greater can be conceived is in the understanding, since when he hears this, he understands it; and whatever is understood is in the understanding. And certainly that than which a greater cannot be conceived cannot be in the understanding alone. For if it is even in the understanding alone, it can be conceived to exist in reality also, which is greater. Thus if that than which a greater cannot be conceived is in the understanding alone, then that than which a greater cannot be conceived is itself that than which a greater can be conceived. But surely this cannot be. Thus without doubt something than which a greater cannot be conceived exists, both in the understanding and in reality."
The argument is ingenious. But there is something wrong about it. And opinon is very divided on what exactly is wrong. Kant criticised the argument with his notion of existence as a "linguistic predicate" not a "real predicate". Anyway one chooses to attack (or defend) Anselm's version of the ontological argument, something is wrong with it. But a stronger version of Anselm's argument can be found. The philosopher Norman Malcom has pointed out that in the Proslagion Anselm argued that if a necessary being could exist, then it must exist, because it is a contradiction to assert that a necessary being does not exist. This variant of Anselm's version of the ontological argument (although still fishy) escapes many of the attacks that the more well known version has recieved. I have presented the oldest ontological argument (even though it is one of the weakest) to (another "again") avoid confusion. Much more convincing ontological arguments are out there like the modern ones formulated by G?del, Alvin Plantinga, Norman Malcom, Oppenheimer and Zalta, Hawthorne and a few others. But these arguments are still problematic.