If you have FAITH in God you will know that he is omnipotent. If you don't know God it is because you don't have FAITH!

End of argument!

The best argument for the existence of an omnipotent God is the existence of the universe itself. Something exists, rather than nothing. Whatever it is that can create something out of nothing can presumably dictate anything at all to that something. It is not constrained even by logic, since logic itself would tell you that nothing can come of nothing, and we chucked that right at the beginning.

The problem with this argument is that it's not an argument at all. It's a definition: God is defined to be that which created the universe ex nihilo. It does not identify that thing with any of the other properties variously ascribed to God: God loves you, God hates evil, God sent the world his only begotten son, God doesn't want you to eat shrimp (godhatesshrimp.com). If the origin of the universe turns out to be, say, the collision of two 11-dimensional branes in Hilbert space, then God didn't really tell Noah to gather up animals two by two or cause Hurricane Katrina to strike New Orleans. So in the end, the argument doesn't really resolve what you want it to resolve.

Still, it's the best argument I know of for the notion that the universe is not governed solely by deterministic mechanical laws. There was at least one instant at the beginning where none of the laws as we currently understand them apply, and science is almost completely at a loss for what to say about it. Positing a God there is as good a solution as any. The only problem is that it's a completely useless solution, holding at that instant and telling you absolutely not one single thing else.