If God can do anything, can He create a rock that is so heavy, He cannot lift it?
Updated 27-Dec-10
That's an entertaining thought. However, did you know that there are some things that God can't do? He is self-limiting. Even as humans, we all limit ourselves from doing certain things, especially things that are a waste of time. God only does what He wants to do (Hey, you can do that when you're God). He can't sin, lie, or do stupid-human-tricks (if I can borrow a term from David Letterman) to entertain us. God is an all-powerful Spirit (Jn 4.24) & not confined by the physical matter or physics that He created. He is magnificent & awesome; worthy of all respect & worship. All will give an account to Him who is ready to judge the living & the dead (1 Pet 4.5).
So I guess the answer is no. God only concerns Himself with what He wants to do. He does all things with a purpose - His purpose. We may not always know or understand why (Dt 29.29, Isa 55.8-9). One thing He does want to do is reveal Himself to people who honestly want to know Him (1 Tim 2.3-4).
"It remains true that all things are possible with God: the intrinsic impossibilities are not things but nonentities. It is no more possible for God than for the weakest of His creatures to carry out both of two mutually exclusive alternatives; not because His power meets an obstacle, but because nonsense remains nonsense even when we talk it about God." - C.S. Lewis in The Problem of Pain