There is one argument that is kinda fun.
Assuming that God is:
a) Omnipotent
b) Omni-benevolent
c) Omniscient
Prove God does not exist.
If an all knowing, all good, all powerful God exists, then how do we account for the existence of evil. There is no way an all good, all powerful, and all knowing God would allow evil to exist; the very existence of evil contradicts this definition of God.
However, this is not the God of any Bible, that is for sure. In the Bible, God is really not all good. He is selfish, etc.
St. Anselm's argument is meh at best. People base the argument off the idea that to be able to not exist and still be all powerful, etc, is better than to exist. Yet one cannot exist and not exist at the same time. This argument uses that contradiction to defeat the existence of God, but like I said... I don't really like it.
Finally, just to add something really relevant... please DEFINE God before you argue for or against it's existence. Nothing irks me more than someone giving an invalid argument with no information on what is being proven etc.